19Miller, Mirka
9Baca, Martin
7Ryan, Joe
5Lin, Yuqing
4Slamin,
3Baskoro, Edy
3Simanjuntak, Rinovia
2Balbuena, Camino
2Barker, Ewan
2Slamet, Surjadi
1Ahmad, Abeed
1Cholily, Yus Mochamad
1Das, K. C.
1Fernau, Henning
1Jendrol, Stanislav
1MacDougall, James
1Manyem, Prabhu
1Patel, Deval
1Tkac, M.

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150101 Pure Mathematics
7Antimagic labeling
5Graph theory
4Magic labeling
3Graph
20103 Numerical and Computational Mathematics
20802 Computation Theory and Mathematics
2Integer programming
2Labeling
2Set theory
2Sum labelling
10104 Statistics
1Adjacency
1Antimagic
1Antiprisms
1Australian Digital Thesis
1Bijection
1Computation theory
1Computational complexity
1Computational methods

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Format Type

(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

A sum labelling for the generalised friendship graph

- Fernau, Henning, Ryan, Joe, Sugeng, Kiki Ariyanti

**Authors:**Fernau, Henning , Ryan, Joe , Sugeng, Kiki Ariyanti**Date:**2008**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 308, no. 5-6 (2008), p. 734-740**Full Text:**false**Reviewed:****Description:**We provide an optimal sum labelling scheme for the generalised friendship graph, also known as the flower (a symmetric collection of cycles meeting at a common vertex) and show that its sum number is 2. © 2007 Elsevier B.V. All rights reserved.**Description:**C1

An application of sum labeling for the access structure in a secret sharing scheme

- Miller, Mirka, Sugeng, Kiki Ariyanti, Slamet, Surjadi

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti , Slamet, Surjadi**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at INACISC Indonesia Cryptology and Information Security Conference, Jakarta, Indonesia : 30th - 31st March, 2005**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001405

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

- Balbuena, Camino, Barker, Ewan, Lin, Yuqing, Miller, Mirka, Sugeng, Kiki Ariyanti

**Authors:**Balbuena, Camino , Barker, Ewan , Lin, Yuqing , Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 306, no. 16 (2006), p. 1817-1829**Full Text:**false**Reviewed:****Description:**Let G be a graph of order n and size e. A vertex-magic total labeling is an assignment of the integers 1, 2, ..., n + e to the vertices and the edges of G, so that at each vertex, the vertex label and the labels on the edges incident at that vertex, add to a fixed constant, called the magic number of G. Such a labeling is a-vertex consecutive magic if the set of the labels of the vertices is { a + 1, a + 2, ..., a + n }, and is b-edge consecutive magic if the set of labels of the edges is { b + 1, b + 2, ..., b + e }. In this paper we prove that if an a-vertex consecutive magic graph has isolated vertices then the order and the size satisfy (n - 1)**Description:**C1**Description:**2003001604

Construction of super edge magic total graphs

- Xie, Wei, Sugeng, Kiki Ariyanti

**Authors:**Xie, Wei , Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, 18-21 September 2005, Ballarat, Australia, Ballarat, Victoria : 18th September, 2005**Full Text:****Reviewed:****Description:**E1**Description:**2003001433

**Authors:**Xie, Wei , Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, 18-21 September 2005, Ballarat, Australia, Ballarat, Victoria : 18th September, 2005**Full Text:****Reviewed:****Description:**E1**Description:**2003001433

Exclusive sum labeling of graphs

- Miller, Mirka, Patel, Deval, Ryan, Joe, Sugeng, Kiki Ariyanti, Slamin,, Tuga, Mauritsius

**Authors:**Miller, Mirka , Patel, Deval , Ryan, Joe , Sugeng, Kiki Ariyanti , Slamin, , Tuga, Mauritsius**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 137-148**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001402

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

Magic and antimagic labeling of graphs

**Authors:**Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Thesis , PhD**Full Text:****Description:**"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling."**Description:**Doctor of Philosophy

**Authors:**Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Thesis , PhD**Full Text:****Description:**"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling."**Description:**Doctor of Philosophy

New constructions of A-magic graphs using labeling matrices

- Sugeng, Kiki Ariyanti, Miller, Mirka

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008), p. 147-151**Full Text:**false**Reviewed:**

On consecutive edge magic total labeling of graphs

- Sugeng, Kiki Ariyanti, Miller, Mirka

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Discrete Algorithms Vol. 6, no. 1 (2008), p. 59-65**Full Text:**false**Reviewed:****Description:**Let G = (V, E) be a finite (non-empty) graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection**Description:**C1

On several classes of monographs

- Sugeng, Kiki Ariyanti, Ryan, Joe

**Authors:**Sugeng, Kiki Ariyanti , Ryan, Joe**Date:**2007**Type:**Text , Journal article**Relation:**Australasian Journal of Combinatorics Vol. 37, no. (2007), p. 277-284**Full Text:**false**Reviewed:****Description:**C1**Description:**2003004943

On the degrees of a strongly vertex-magic graph

- Balbuena, Camino, Barker, Ewan, Das, K. C., Lin, Yuqing, Miller, Mirka, Ryan, Joe, Slamin,, Sugeng, Kiki Ariyanti, Tkac, M.

**Authors:**Balbuena, Camino , Barker, Ewan , Das, K. C. , Lin, Yuqing , Miller, Mirka , Ryan, Joe , Slamin, , Sugeng, Kiki Ariyanti , Tkac, M.**Date:**2006**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 306, no. 6 (2006), p. 539-551**Full Text:**false**Reviewed:****Description:**Let G=(V,E) be a finite graph, where |V|=n≥2 and |E|=e≥1. A vertex-magic total labeling is a bijection λ from V∪E to the set of consecutive integers {1,2,...,n+e} with the property that for every v∈V, λ(v)+∑w∈N(v)λ(vw)=h for some constant h. Such a labeling is strong if λ(V)={1,2,...,n}. In this paper, we prove first that the minimum degree of a strongly vertex-magic graph is at least two. Next, we show that if 2e≥10n2-6n+1, then the minimum degree of a strongly vertex-magic graph is at least three. Further, we obtain upper and lower bounds of any vertex degree in terms of n and e. As a consequence we show that a strongly vertex-magic graph is maximally edge-connected and hamiltonian if the number of edges is large enough. Finally, we prove that semi-regular bipartite graphs are not strongly vertex-magic graphs, and we provide strongly vertex-magic total labeling of certain families of circulant graphs. © 2006 Elsevier B.V. All rights reserved**Description:**C1**Description:**2003001603

Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2005)

- Ryan, Joe, Manyem, Prabhu, Sugeng, Kiki Ariyanti, Miller, Mirka

**Authors:**Ryan, Joe , Manyem, Prabhu , Sugeng, Kiki Ariyanti , Miller, Mirka**Date:**2005**Type:**Text , Conference proceedings**Full Text:**false

Properties of consecutive edge magic total graphs

- Miller, Mirka, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Victoria : 18th -21st September, 2005**Full Text:****Reviewed:****Description:**E1**Description:**2003001404

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Victoria : 18th -21st September, 2005**Full Text:****Reviewed:****Description:**E1**Description:**2003001404

Relationship between adjacency matrices and super (a,d)-edge-antimagic total labeling of graphs

- Miller, Mirka, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 71-82**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001403

Sum graph based access structure in a secret sharing scheme

- Miller, Mirka, Slamet, Surjadi, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Slamet, Surjadi , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Prime Research in Mathematics Vol. 2, no. (2006), p. 113-119**Full Text:****Reviewed:****Description:**Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorised subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct numbers, usually positive integers, such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label is L(w) = L(u) + L(v). In this paper, we will show how sum labeling can be used for representing the graphs of the access structures of a secret sharing scheme. We will combine a known secret sharing scheme such as the classical Shamir scheme with a graph access structure represented using sum graph labeling to obtain a new secret sharing scheme.**Description:**C1**Description:**2003001595

**Authors:**Miller, Mirka , Slamet, Surjadi , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Prime Research in Mathematics Vol. 2, no. (2006), p. 113-119**Full Text:****Reviewed:****Description:**Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorised subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct numbers, usually positive integers, such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label is L(w) = L(u) + L(v). In this paper, we will show how sum labeling can be used for representing the graphs of the access structures of a secret sharing scheme. We will combine a known secret sharing scheme such as the classical Shamir scheme with a graph access structure represented using sum graph labeling to obtain a new secret sharing scheme.**Description:**C1**Description:**2003001595

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

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