130101 Pure Mathematics
8Antimagic labeling
3Graph labeling
2Plane graph
2Super (a,d)-edge-antimagic total labeling
1(A,d)-edge-antimagic total labeling
10104 Statistics
108 Information and Computing Sciences
10802 Computation Theory and Mathematics
1Antiprisms
1Edge assignment
1Edge irregular total
1Edge-antimagic labeling
1Edge-antimagicness
1Edge-weight
1Edges
1Face weight
1Graph
1Graphs
1Grid

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(a,d)-edge-antimagic total labelings of caterpillars

- Miller, Mirka, Sugeng, Kiki Ariyanti, Slamin,, Baca, Martin

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti , Slamin, , Baca, Martin**Date:**2005**Type:**Text , Journal article**Relation:**Combinatorial Geometry and Graph Theory, LNCS 3330, Lecture Notes in Computer Science, Indonesia-Japan Joint Conference IJCCGGT 2003, Bandung, Indonesia, September 2003, Revised Selected Papers Vol. 3330, no. (2005), p. 169-180**Full Text:**false**Reviewed:****Description:**For a graph G = (V,E), a bijection g from V (G)∪E(G) into {1, 2, ..., |V (G)|+|E(G)|} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a, d)-edge-antimagic total labeling g is called super (a, d)-edge-antimagic total if g(V (G)) = {1, 2, ..., |V (G)|}. We study super (a, d)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr .**Description:**C1**Description:**2003001412

Antimagic labeling of disjoint union of s-crowns

- Baca, Martin, Dafik, Miller, Mirka, Ryan, Joe

**Authors:**Baca, Martin , Dafik , Miller, Mirka , Ryan, Joe**Date:**2009**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 79, no. (2009), p. 193-205**Full Text:**false**Reviewed:****Description:**A graph G is called (a, d)-edge-antimagic total if it admits a labeling of the vertices and edges by pairwise distinct integers of 1,2,..., |V(G)| + |E(G)| such that the edge-weights, w(uÏ…) = f(u) + f(Ï…) + f(uÏ…), uv âˆˆ E(G), form an arithmetic sequence with the first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. A construction of super (a, d)-edge-antimagic total labelings of some disconnected graphs are described.

- Baca, Martin, Lin, Yuqing, Miller, Mirka

**Authors:**Baca, Martin , Lin, Yuqing , Miller, Mirka**Date:**2007**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 72, no. (2007), p. 65-75**Full Text:**false**Reviewed:****Description:**In this paper we deal with the problem of labeling the vertices, edges and faces of a grid graph by the consecutive integers from 1 to |V| + |E| + |F| in such a way that the label of a face and the labels of the vertices and edges surrounding that face all together add up to a weight of that face. These face weights then form an arithmetic progression with common difference d.**Description:**C1**Description:**2003004808

Antimagic valuations for the special class of plane graphs

- Baca, Martin, Baskoro, Edy, Miller, Mirka

**Authors:**Baca, Martin , Baskoro, Edy , Miller, Mirka**Date:**2005**Type:**Text , Journal article**Relation:**Lecture Notes in Computer Science Vol. 3350, no. (2005), p. 58-64**Full Text:**false**Reviewed:****Description:**We deal with the problem of labeling the vertices, edges and faces of a special class of plane graphs with 3-sided internal faces in such a way that the label of a face and the labels of the vertices and edges surrounding that face all together add up to the weight of that face. These face weights then form an arithmetic progression with common difference d.**Description:**C1**Description:**2003001410

Conjectures and open problems on face antimagic evaluations of graphs

- Miller, Mirka, Baca, Martin, Baskoro, Edy, Cholily, Yus Mochamad, Jendrol, Stanislav, Lin, Yuqing, Ryan, Joe, Simanjuntak, Rinovia, Slamin,, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Baca, Martin , Baskoro, Edy , Cholily, Yus Mochamad , Jendrol, Stanislav , Lin, Yuqing , Ryan, Joe , Simanjuntak, Rinovia , Slamin, , Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Indonesian Mathematical Society MIHMI Vol. 11, no. 2 (2005), p. 175-192**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001408

- Baca, Martin, Lin, Yuqing, Miller, Mirka, Youssef, Maged

**Authors:**Baca, Martin , Lin, Yuqing , Miller, Mirka , Youssef, Maged**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1232-1244**Full Text:**false**Reviewed:****Description:**For a graph G = (V, E), a bijection g from V(G) boolean OR E(G) into {1, 2,..., vertical bar V(G)vertical bar + vertical bar E(G)vertical bar} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy E E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edge-antimagic total labeling is called super (a, d)-edge-antimagic total if g(V(G)) = {1, 2,..., vertical bar V(G)vertical bar}. We study super (a, d)-edge-antimagic properties of certain classes of graphs, including friendship graphs, wheels, fans, complete graphs and complete bipartite graphs. (c) 2006 Elsevier B.V. All rights reserved.**Description:**2003004910

Edge-antimagic total labeling of disjoint union of caterpillars

- Baca, Martin, Dafik, Miller, Mirka, Ryan, Joe

**Authors:**Baca, Martin , Dafik , Miller, Mirka , Ryan, Joe**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008 2008), p. 61-70**Full Text:**false**Reviewed:**

Face antimagic labelings of prisms

- Sugeng, Kiki Ariyanti, Miller, Mirka, Baca, Martin

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin**Date:**2006**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 71, no. (Nov 2006), p. 269-286**Full Text:**false**Reviewed:****Description:**This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and labels of vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every number s, the s-sided face weights form an arithmetic progression of difference d. In this paper, we investigate d-antimagic labelings for prism for d is an element of {7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 24, 26,27,30,36).**Description:**C1

Further results in d-antimagic labelings of antiprisms

- Lin, Yuqing, Ahmad, Abeed, Miller, Mirka, Sugeng, Kiki Ariyanti, Baca, Martin

**Authors:**Lin, Yuqing , Ahmad, Abeed , Miller, Mirka , Sugeng, Kiki Ariyanti , Baca, Martin**Date:**2004**Type:**Text , Conference paper**Relation:**Paper presented at AWOCA 2004: Fifteenth Australasian Workshop on Combinatorial Algorithms, Ballina, New South Wales : 6-9th July, 2004**Full Text:**false**Reviewed:****Description:**E1**Description:**2003000900

On antimagic labelings of disjoint union of complete s-partite graphs

- Dafik, Miller, Mirka, Ryan, Joe, Baca, Martin

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008 2008), p. 41-49**Full Text:****Reviewed:****Description:**By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) u E(G) onto the set. { 1, 2, ... ,ǀV(C)ǀ+IE(G)I} such that the set of all the edge-weights, w(uv) ,.... f(u) + f(uv) + f(v), uv C E (G), is {a, a+ d, a+ 2d, . . . , a + (lE(G)I-1)d}, for two integers a > 0 and d

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008 2008), p. 41-49**Full Text:****Reviewed:****Description:**By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) u E(G) onto the set. { 1, 2, ... ,ǀV(C)ǀ+IE(G)I} such that the set of all the edge-weights, w(uv) ,.... f(u) + f(uv) + f(v), uv C E (G), is {a, a+ d, a+ 2d, . . . , a + (lE(G)I-1)d}, for two integers a > 0 and d

On d-antimagic labelings of prisms

- Lin, Yuqing, Slamin,, Baca, Martin, Miller, Mirka

**Authors:**Lin, Yuqing , Slamin, , Baca, Martin , Miller, Mirka**Date:**2004**Type:**Text , Journal article**Relation:**Ars Combinatoria: A Canadian Journal of Combinatorics Vol. 72, no. (2004), p. 65-76**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000907

On irregular total labellings

- Baca, Martin, Jendrol, Stanislav, Miller, Mirka, Ryan, Joe

**Authors:**Baca, Martin , Jendrol, Stanislav , Miller, Mirka , Ryan, Joe**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1378-1388**Full Text:****Reviewed:****Description:**Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. (c) 2006 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003004909

**Authors:**Baca, Martin , Jendrol, Stanislav , Miller, Mirka , Ryan, Joe**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1378-1388**Full Text:****Reviewed:****Description:**Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. (c) 2006 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003004909

Super (a,d)-vertex-antimagic total labelings

- Miller, Mirka, Sugeng, Kiki Ariyanti, Lin, Yuqing, Baca, Martin

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti , Lin, Yuqing , Baca, Martin**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 91-102**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001401

Super antimagic total labeling of graphs

- Sugeng, Kiki Ariyanti, Miller, Mirka, Baca, Martin

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 76, no. (2008), p. 161-171**Full Text:**false**Reviewed:****Description:**Let G = (V, E) be a simple, finite and undirected graph with v vertices and e edges, A graph labeling is a mapping from elements of a graph to a set of numbers (usually positive integers). If the domain of the mapping is the set of vertices (or edges) then the labeling is called vertex-labeling (or edge-labeling). If the domain of the mapping is the set of vertices and edges then the labeling is called total labeling. The sum of all labels associated with a graph element is called the weight of the element. If the weights of vertices (or the weights of edges) form an arithmetic progression starting at a and with difference d, then the labeling is called (a, d)-vertex-antimagic (or (a, d)-edge-antimagic). Such a labeling is called v-super (or e-super) if the smallest labels appear on the vertices (or edges). In this paper we present new results for v-super vertex-antimagic total and e-super edge-antimagic total labeling.**Description:**C1

Super edge-antimagic labelings of the generalized Petersen graph P(n, (n-1)/2))

- Baca, Martin, Baskoro, Edy, Simanjuntak, Rinovia, Sugeng, Kiki Ariyanti

**Authors:**Baca, Martin , Baskoro, Edy , Simanjuntak, Rinovia , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 70, no. (Jul 2006), p. 119-127**Full Text:**false**Reviewed:****Description:**An (a,d)-edge-antimagic total labeling of G is a one-to-one mapping f taking the vertices and edges onto 1, 2,..., vertical bar V (G)vertical bar + vertical bar E(G)vertical bar so that the edge-weights w(xy) = f(x) + f(y) + f(xy), xy is an element of E(G), form an arithmetic progression with initial term a and common difference d. An (a, d)-edge-antimagic total labeling is called super (a,d)-edge-antimagic total if f(V(G)) = {1, 2,..., vertical bar V(G)vertical bar}. This paper considers such labelings applied to cycles and generalized Petersen graphs.**Description:**C1**Description:**2003001832

Super edge-antimagic total labeling

- Sugeng, Kiki Ariyanti, Miller, Mirka, Baca, Martin

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin**Date:**2006**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 71, no. (2006), p. 131-141**Full Text:**false**Reviewed:****Description:**A (p, q)-graph G is (a, d)-edge-antimagic total if there exists a bijective function f : V(G) ∪ E(G) → {1,2,...,p + q} such that the edge-weights w(uv) = f(u) + f(v) + f(uv), uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. Moreover, G is said to be super (a, d)-edge-antimagic total if f(V(G)) = {1,2,..., p}. In this paper we study the super (a,d)-edge-antimagic total properties of certain classes of graphs, including ladders, generalized prisms and antiprisrns.**Description:**C1**Description:**2003001596

Super edge-antimagic total labelings of mKn,n,n

- Dafik, Miller, Mirka, Ryan, Joe, Baca, Martin

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2011**Type:**Text , Journal article**Relation:**Ars Combinatoria Vol. 101, no. (2011), p. 97-107**Full Text:**false**Reviewed:****Description:**An (a, d)-edge-antimagic total labeling on (p, q)-graph G is a one-to-one map f from V(G) ∪ E(G) onto the integers 1,2,...,p + q with the property that the edge-weights, w(uv) = f(u)+f(v)+f(uv) where uv Îµ E(G), form an arithmetic progression starting from a and having common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super (a, d)-edge-antimagic total labeling of disjoint union of multiple copies of complete tripartite graph and disjoint union of stars.**Description:**An (a, d)-edge-antimagic total labeling on (p, q)-graph G is a one-to-one map f from V(G) ∪ E(G) onto the integers 1,2,...,p + q with the property that the edge-weights, w(uv) = f(u)+f(v)+f(uv) where uv Îµ E(G), form an arithmetic progression starting from a and having common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super (a, d)-edge-antimagic total labeling of disjoint union of multiple copies of complete tripartite graph and disjoint union of stars.

Super edge-antimagicness for a class of disconnected graphs

- Dafik, Miller, Mirka, Ryan, Joe, Baca, Martin

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2006**Type:**Text , Conference paper**Relation:**Paper presented at AWOCA 2006, 17th Australasian Workshop on Combinatorial Algorithms, Uluru, Australia : 13th July, 2006 p. 67-75**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001916

Survey of edge antimagic labelings of graphs

- Miller, Mirka, Baca, Martin, Baskoro, Edy, Ryan, Joe, Simanjuntak, Rinovia, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Baca, Martin , Baskoro, Edy , Ryan, Joe , Simanjuntak, Rinovia , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Indonesian Mathematical Society, MIHMI Vol. 12, no. 1 (2006), p. 113-130**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001600

Vertex-magic total labeling of generalized Petersen graphs and convex polytopes

- Miller, Mirka, Baca, Martin, MacDougall, James

**Authors:**Miller, Mirka , Baca, Martin , MacDougall, James**Date:**2006**Type:**Text , Journal article**Relation:**JCMCC Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 59, no. (2006), p. 89-99**Full Text:****Reviewed:****Description:**To date the study of graph labellings has focused on nding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic labellings for which all graphs admit such a labelling. In particular we consider two types of labellings of the vertices and edges of a graph with distinct positive integers: (1) for every edge the sum of its label and those of its endvertices is some constant (pseudo edge-magic); and (2) for every vertex the sum of its label and those of the edges incident to it is some constant (pseudo vertex-magic). Our aim is to minimise the constant, called the magic number, associated with the labelling. We present lower and upper bounds on the magic number in pseudo edge-magic and pseudo vertex-magic labellings of complete graphs, trees and arbitrary graphs. In a number of cases these bounds are within a constant factor.**Description:**C1**Description:**2003001602

**Authors:**Miller, Mirka , Baca, Martin , MacDougall, James**Date:**2006**Type:**Text , Journal article**Relation:**JCMCC Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 59, no. (2006), p. 89-99**Full Text:****Reviewed:****Description:**To date the study of graph labellings has focused on nding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic labellings for which all graphs admit such a labelling. In particular we consider two types of labellings of the vertices and edges of a graph with distinct positive integers: (1) for every edge the sum of its label and those of its endvertices is some constant (pseudo edge-magic); and (2) for every vertex the sum of its label and those of the edges incident to it is some constant (pseudo vertex-magic). Our aim is to minimise the constant, called the magic number, associated with the labelling. We present lower and upper bounds on the magic number in pseudo edge-magic and pseudo vertex-magic labellings of complete graphs, trees and arbitrary graphs. In a number of cases these bounds are within a constant factor.**Description:**C1**Description:**2003001602

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