Super edge-antimagicness for a class of disconnected graphs
- 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
On the nonexistence of graphs of diameter 2 and defect 2
- Authors: Miller, Mirka , Nguyen, Minh Hoang , Pineda-Villavicencio, Guillermo
- Date: 2009
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 71, no. (2009), p. 5-20
- Full Text: false
- Reviewed:
- Description: In 1960, Hoffman and Singleton investigated the existence of Moore graphs of diameter 2 (graphs of maximum degree d and d² + 1 vertices), and found that such graphs exist only for d = 2; 3; 7 and possibly 57. In 1980, Erdös et al., using eigenvalue analysis, showed that, with the exception of C4, there are no graphs of diameter 2, maximum degree d and d² vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d² - 1 vertices do not exist for most values of d with d ≥ 6, and conjecture that they do not exist for any d ≥ 6.
- Description: 2003007893
All (k;g)-cages are k-edge-connected
- Authors: Lin, Yuqing , Miller, Mirka , Rodger, Chris
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Graph Theory Vol. 48, no. 3 (2005), p. 219-227
- Full Text: false
- Reviewed:
- Description: A (k;g)-cage is a k-regular graph with girth g and with the least possible number of vertices. In this paper, we prove that (k;g)-cages are k-edge-connected if g is even. Earlier, Wang, Xu, and Wang proved that (k;g)-cages are k-edge-connected if g is odd. Combining our results, we conclude that the (k;g)-cages are k-edge-connected. © 2005 wiley Periodicals, Inc.
- Description: C1
Graphs of order two less than the Moore bound
- Authors: Miller, Mirka , Simanjuntak, Rinovia
- Date: 2008
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 308, no. 13 (2008), p. 2810-2821
- Full Text: false
- Reviewed:
- Description: The Moore bound for a directed graph of maximum out-degree d and diameter k is Md,k=1+d+d2++dk. It is known that digraphs of order Md,k (Moore digraphs) do not exist for d>1 and k>1. Similarly, the Moore bound for an undirected graph of maximum degree d and diameter k is . Undirected Moore graphs only exist in a small number of cases. Mixed (or partially directed) Moore graphs generalize both undirected and directed Moore graphs. In this paper, we shall show that all known mixed Moore graphs of diameter k=2 are unique and that mixed Moore graphs of diameter k3 do not exist.
- Description: C1
Delta-optimum exclusive sum labeling of certain graphs with radius one
- Authors: Tuga, Mauritsius , Miller, Mirka
- Date: 2005
- Type: Text , Journal article
- Relation: Lecture Notes in Computer Science Vol. 3330, no. (2005), p. 216-225
- Full Text: false
- Reviewed:
- Description: A mapping
- Description: C1
- Description: 2003001413
On graphs of maximum size with given girth and order
- Authors: Miller, Mirka , Lin, Yuqing , Brankovic, Ljiljana , Tang, Jianmin
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at AWOCA 2006, 17th Australasian Workshop on Combinatorial Algorithms, Uluru, Australia : 13th July, 2006
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003001918
On network security and internet vulnerability
- Authors: Miller, Mirka , Patel, Deval , Patel, Keyurkumar
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at IADIS International Conference on Applied Computing 2005, Volume II, Algarve, Portugal : 22nd - 25th February, 2005
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003001409
Antimagic labeling of disjoint union of s-crowns
- 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(uυ) = f(u) + f(υ) + f(uυ), uv ∈ 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.
On d-antimagic labelings of prisms
- 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 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
- Reviewed:
- Description: E1
- Description: 2003000902
On non-polynomiality of XOR over Zn2
- Authors: Grosek, Otokar , Miller, Mirka , Ryan, Joe
- Date: 2004
- Type: Text , Journal article
- Relation: Tatra Mountains Mathematical Publications Vol. 29, no. (2004), p. 183-191
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003000905
Two new families of large compound graphs
- Authors: Marti, J. Gomez , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Networks Vol. 47, no. 3 (2006), p. 140-146
- Full Text: false
- Reviewed:
- Description: A question of special interest in graph theory is the design of large graphs. Specifically, we want to find constructions of graphs with order as large as possible for a given degree A and diameter D. Two generalizations of two large compound graphs are proposed in this article. Three particular cases of these families of graphs presented here allow us to improve the order for the entries (15, 7), (13, 10), and (15, 10) in the table of the largest known (Δ, D)-graphs. © 2006 Wiley Periodicals, Inc.
- Description: C1
- Description: 2003001599
Characterization of eccentric digraphs
- Authors: Gimbert, Joan , Lopez, Nacho , Miller, Mirka , Ryan, Joe
- Date: 2006
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 306, no. 2 (2006), p. 210-219
- Full Text: false
- Reviewed:
- Description: The eccentric digraph ED(G) of a digraph G represents the binary relation, defined on the vertex set of G, of being 'eccentric'; that is, there is an arc from u to v in ED(G) if and only if v is at maximum distance from u in G. A digraph G is said to be eccentric if there exists a digraph H such that G=ED(H). This paper is devoted to the study of the following two questions: what digraphs are eccentric and when the relation of being eccentric is symmetric. We present a characterization of eccentric digraphs, which in the undirected case says that a graph G is eccentric iff its complement graph G is either self-centered of radius two or it is the union of complete graphs. As a consequence, we obtain that all trees except those with diameter 3 are eccentric digraphs. We also determine when ED(G) is symmetric in the cases when G is a graph or a digraph that is not strongly connected. Crown Copyright © 2006 Published by Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001601
Cordial labelling of butterfly networks and mesh of trees
- Authors: Miller, Mirka , Rajan, Bharati , Rajasingh, Indra , Manuel, Paul
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at AWOCA 2006, 17th Australasian Workshop on Combinatorial Algorithms, Uluru, Australia : 13th July, 2006
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003001646
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
Antimagic labelings of grids
- 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
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
Managing privacy, trust, security, and context relationships using weighted graph representations
- Authors: Skinner, Geoff , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Transactions on Information Science and Applications Vol. 3, no. 2 (2006), p. 283-290
- Full Text: false
- Reviewed:
- Description: Determining who has access to personal data is an ongoing problem facing information system entities. The establishment of trust and its representation for known and unknown entities within the system further complicates access control rights allocation. One unique solution is through the application of graph representation to aid in the identification and management of privacy, trust and security requirements. Graphs provide a much better mental map than would textual information. In this paper we use graphs to represent informational relations concerning trust levels between entities for privacy and security requirements.
- Description: C1
- Description: 2003001598
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