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
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
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- Description: E1
- Description: 2003000902
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
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 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
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
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
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- 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
- 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
Consecutive magic graphs
- 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
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
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
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- Description: E1
- Description: 2003001404
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
On consecutive edge magic total labeling of graphs
- 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
(a,d)-edge-antimagic total labelings of caterpillars
- 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
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- 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
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
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
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:
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