Security issues in statistical databases and implementation of audit expert
- Authors: Ahmad, Abeed , Miller, Mirka
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICCC 2004: International Conference on Computers and Communications, Baile Felix Spa-Oradea, Romania : 27th - 29th May, 2004
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000899
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.
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
On irregular total labellings
- 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
Antimagic valuations for the special class of plane graphs
- 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
Edge-antimagic graphs
- 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
- 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:
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
A lower bound on the order of regular graphs with given girth pair
- Authors: Balbuena, Camino , Jiang, T. , Lin, Yuqing , Marcote, Xavier , Miller, Mirka
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Graph Theory Vol. 55, no. 2 (2007), p. 153-163
- Full Text: false
- Reviewed:
- Description: The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and Kovács [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209-218]. A (
- Description: C1
- Description: 2003004727
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
Diameter-sufficient conditions for a graph to be super-restricted connected
- Authors: Balbuena, Camino , Lin, Yuqing , Miller, Mirka
- Date: 2007
- Type: Text , Journal article
- Relation: Discrete Applied Mathematics Vol. , no. (2007), p.
- Full Text: false
- Reviewed:
- Description: A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G - X must have at least two vertices. The restricted connectivity
- Description: C1
Complete characterization of almost moore digraphs of degree three
- Authors: Baskoro, Edy , Miller, Mirka , Siran, Jozef , Sutton, Martin
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Graph Theory Vol. 48, no. 2 (2005), p. 112-126
- Full Text: false
- Reviewed:
- Description: It is well known that Moore digraphs do not exist except for trivial cases (degree 1 or diameter 1), but there are digraphs of diameter two and arbitrary degree which miss the Moore bound by one. No examples of such digraphs of diameter at least three are known, although several necessary conditions for their existence have been obtained. In this paper, we prove that digraphs of degree three and diameter k ≥ 3 which miss the Moore bound by one do not exist. © 2004 Wiley Periodicals, Inc.
- Description: C1
- Description: 2003000904
Enumerations of vertex orders of almost Moore digraphs with selfrepeats
- Authors: Baskoro, Edy , Cholily, Yus Mochamad , Miller, Mirka
- Date: 2008
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 308, no. 1 (2008), p. 123-128
- Full Text: false
- Reviewed:
- Description: An almost Moore digraph G of degree d > 1, diameter k > 1 is a diregular digraph with the number of vertices one less than the Moore bound. If G is an almost Moore digraph, then for each vertex u ∈ V (G) there exists a vertex v ∈ V (G), called repeat of u and denoted by r (u) = v, such that there are two walks of length ≤ k from u to v. The smallest positive integer p such that the composition rp (u) = u is called the order of u. If the order of u is 1 then u is called a selfrepeat. It is known that if G is an almost Moore digraph of diameter k ≥ 3 then G contains exactly k selfrepeats or none. In this paper, we propose an exact formula for the number of all vertex orders in an almost Moore digraph G containing selfrepeats, based on the vertex orders of the out-neighbours of any selfrepeat vertex. © 2007 Elsevier B.V. All rights reserved.
- Description: C1
On the structure of (d,3)-digraphs containing selfrepeats
- Authors: Baskoro, Edy , Cholily, Yus Mochamad , Miller, Mirka
- 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: 2003000901
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
Open problems in the construction of large directed graphs
- Authors: Dafik , Miller, Mirka , Ryan, Joe , Slamin,
- 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: false
- Reviewed:
- Description: E1
- Description: 2003001352
On antimagic labelings of disjoint union of complete s-partite graphs
- 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
Super edge-antimagic total labelings of mKn,n,n
- 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 ε 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 ε 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.
On bipartite graphs of diameter 3 and defect 2
- Authors: Delorme, Charles , Jorgensen, Leif , Miller, Mirka , Pineda-Villavicencio, Guillermo
- Date: 2009
- Type: Text , Journal article
- Relation: Journal of Graph Theory Vol. 61, no. 4 (2009), p. 271-288
- Full Text:
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- Description: We consider bipartite graphs of degree A<2, diameter D = 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (â–³,3, -2) -graphs. We prove the uniqueness of the known bipartite (3, 3, -2) -graph and bipartite (4, 3, -2)-graph. We also prove several necessary conditions for the existence of bipartite (â–³,3, -2) - graphs. The most general of these conditions is that either â–³ or â–³-2 must be a perfect square. Furthermore, in some cases for which the condition holds, in particular, when â–³ = 6 and â–³ = 9, we prove the non-existence of the corresponding bipartite (â–³,3,-2)-graphs, thus establishing that there are no bipartite (â–³,3, -2)-graphs, for 5
On bipartite graphs of defect 2
- Authors: Delorme, Charles , Jorgensen, Leif , Miller, Mirka , Pineda-Villavicencio, Guillermo
- Date: 2009
- Type: Text , Journal article
- Relation: European Journal of Combinatorics Vol. 30, no. 4 (2009), p. 798-808
- Full Text:
- Reviewed:
- Description: It is known that the Moore bipartite bound provides an upper bound on the order of a connected bipartite graph. In this paper we deal with bipartite graphs of maximum degree