### Further results in d-antimagic labelings of antiprisms

**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

### Super antimagic total labeling of graphs

**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

### New constructions of A-magic graphs using labeling matrices

**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:**

### Super vertex-magic total labelings of graphs

**Authors:**MacDougall, James , Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2004**Type:**Text , Conference paper**Relation:**Paper presented at AWOCA 2004: Fifteenth Australasian Workshop on Combinatorial Algorithms, Ballina, New South Wales : 6th - 9th July, 2004 p. 222–229**Full Text:**false**Reviewed:****Description:**E1**Description:**2003000902

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

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

### Super edge-antimagic total labeling

**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

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

**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

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

**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

### Construction of super edge magic total graphs

**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

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

**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

**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

### Properties of consecutive edge magic total graphs

**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

### Face antimagic labelings of prisms

**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

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

**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

### On several classes of monographs

**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

### Survey of edge antimagic labelings of graphs

**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

### Exclusive sum labeling of graphs

**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

### Sum graph based access structure in a secret sharing scheme

**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

### A sum labelling for the generalised friendship graph

**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

### On the degrees of a strongly vertex-magic graph

**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