(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
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
All (k;g)-cages are edge-superconnected
- Authors: Lin, Yuqing , Miller, Mirka , Balbuena, Camino , Marcote, Xavier
- Date: 2006
- Type: Text , Journal article
- Relation: Networks Vol. 47, no. 2 (2006), p. 102-110
- Full Text: false
- Reviewed:
- Description: A (k;g)-cage is k-regular graph with girth g and with the least possible number of vertices. In this article we prove that (k;g)-cages are edge-superconnected if g is even. Earlier, Marcote and Balbuena proved that (k;g)-cages are edge-superconnected if g is odd [Networks 43 (2004), 54-59]. Combining our results, we conclude that all (k;g)-cages are edge-superconnected. © 2005 Wiley Periodicals, Inc.
- Description: C1
- Description: 2003001830
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
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
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
Calculating the extremal number ex (v ; {C3, C4, ..., Cn})
- Authors: Tang, Jianmin , Lin, Yuqing , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Electronic Notes in Discrete Mathematics Vol. 27, no. (2006), p. 101-102
- Full Text: false
- Reviewed:
- Description: This paper introduces and analyzes a parallel method of simulated annealing. Borrowing from genetic algorithms, an effective combination of simulated annealing and genetic algorithms, called parallel recombinative simulated annealing, is developed. This new algorithm strives to retain the desirable asymptotic convergence properties of simulated annealing, while adding the populations approach and recombinative power of genetic algorithms. The algorithm iterates a population of solutions rather than a single solution, employing a binary recombination operator as well as a unary neighborhood operator. Proofs of global convergence are given for two variations of the algorithm. Convergence behavior is examined, and empirical distributions are compared to Boltzmann distributions. Parallel recombinative simulated annealing is amenable to straightforward implementation on SIMD, MIMD, or shared-memory machines. The algorithm, implemented on the CM-5, is run repeatedly on two deceptive problems to demonstrate the added implicit parallelism and faster convergence which can result from larger population sizes.
- Description: C1
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
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
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
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
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
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
Divisibility conditions in almost Moore digraphs with selfrepeats
- Authors: Teska, Jakub , Kuzel, Roman , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Electronic Notes in Discrete Mathematics Vol. 24, no. (2006), p. 161-163
- Full Text: false
- Reviewed:
- Description: Moore digraph is a digraph with maximum out-degree d, diameter k and order Md, k = 1 + d + ... + dk. Moore digraphs exist only in trivial cases if d = 1 (i.e., directed cycle Ck) or k = 1 (i.e., complete symmetric digraph). Almost Moore digraphs are digraphs of order one less than Moore bound. We shall present new properties of almost Moore digraphs with selfrepeats from which we prove nonexistence of almost Moore digraphs for some k and d. © 2006 Elsevier B.V. All rights reserved.
- Description: C1
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:
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
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
Exclusive sum labelings of trees
- Authors: Miller, Mirka , Tuga, Mauritsius , Ryan, Joe , Ryjacek, Zdenek
- Date: 2005
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 109-121
- Full Text: false
- Reviewed:
- Description: The notions of
- Description: C1
- Description: 2003001406