Moore bound for mixed networks
- Authors: Nguyen, Minh Hoang , Miller, Mirka
- Date: 2008
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 308, no. 23 (Dec 2008), p. 5499-5503
- Full Text: false
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- Description: Mixed graphs contain both undirected as well as directed links between vertices and therefore are an interesting model for interconnection communication networks. In this paper, we establish the Moore bound for mixed graphs, which generalizes both the directed and the undirected Moore bound. Crown Copyright (C) 2007 Published by Elsevier B.V. All rights reserved.
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:
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
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- 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
On antimode graphs
- Authors: Marshall, Kim , Ryan, Joe
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 65, no. (May 2008 2008), p. 51-60
- Full Text: false
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- Description: The term mode graph was introduced by Boland, Kauffman and Panroug [2] to defiue a connected graph G such that, for every pair of vertices v, w in G, the number of vertices with eccentricity e(v) is equal to the number of vertices with eccentricity e(w). As a natural extension to this work, the concept of an antimode graph was introduced to describe a graph for which if e(v) ≠ e(w) then the number of vertices with eccentricity e(v) is not equal to the number of vertices with eccentricity e(w). ln this paper we determine the existence of some classes of antimode graphs, namely equisequential and (a, d)-antimode graphs.
On graphs of maximum degree 3 and defect 4
- Authors: Pineda-Villavicencio, Guillermo , Miller, Mirka
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008), p. 25-31
- Full Text: false
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- Description: It is well known that apart from the Petersen graph there are no Moore graphs of degree 3. As a cubic graph must have an even number of vertices, there are no graphs of maximum degree 3 and
On the connectivity of (k, g)-cages of even girth
- Authors: Lin, Yuqing , Balbuena, Camino , Marcote, Xavier , Miller, Mirka
- Date: 2008
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 308, no. 15 (2008), p. 3249-3256
- Full Text: false
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- 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 give a brief overview of the current results on the connectivity of (k,g)-cages and we improve the current known best lower bound on the vertex connectivity of (k,g)-cages for g even. © 2007 Elsevier B.V. All rights reserved.
- Description: C1
On the pro-lie group theorem and the closed subgroup theorem
- Authors: Hofmann, Karl , Morris, Sidney
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Lie Theory Vol. 18, no. 2 (2008), p. 383-390
- Full Text: false
- Reviewed:
- Description: Let H and M be closed normal subgroups of a pro-Lie group G and assume that H is connected and that G/M is a Lie group. Then there is a closed normal subgroup N of G such that N ? M, that G/N is a Lie group, and that HN is closed in G. As a consequence, H/(H ? N) ? HN/N is an isomorphism of Lie groups. © 2008 Heldermann Verlag.
- Description: C1
Structural properties of graphs of diameter 2 with maximal repeats
- Authors: Nguyen, Minh Hoang , Miller, Mirka
- Date: 2008
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 308, no. 11 (Jun 2008), p. 2337-2341
- Full Text: false
- Reviewed:
- Description: It was shown using eigenvalue analysis by Erdos et al. that with the exception of C-4, there are no graphs of diameter 2, of maximum degree d and of order d(2), that is, one less than the Moore bound. These graphs belong to a class of regular graphs of diameter 2, and having certain interesting structural properties, which will be proved in this paper. (c) 2007 Elsevier B.V. All rights reserved.
- Description: C1
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
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- 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
The core of a sequence of fuzzy numbers
- Authors: Aytar, Salih , Pehlivan, Serpil , Mammadov, Musa
- Date: 2008
- Type: Text , Journal article
- Relation: Fuzzy Sets and Systems Vol. 159, no. 24 (2008), p. 3369-3379
- Full Text: false
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- Description: In this paper, based on level sets we define the limit inferior and limit superior of a bounded sequence of fuzzy numbers and prove some properties. We extend the concept of the core of a sequence of complex numbers, first introduced by Knopp in 1930, to a bounded sequence of fuzzy numbers and prove that the core of a sequence of fuzzy numbers is the interval [ν, μ] where ν and μ are extreme limit points of the sequence. © 2008 Elsevier B.V. All rights reserved.
A dual criterion for maximal monotonicity of composition operators
- Authors: Jeyakumar, Vaithilingam , Wu, Zhiyou
- Date: 2007
- Type: Text , Journal article
- Relation: Set-Valued Analysis Vol. 15, no. 3 (2007), p. 265-273
- Full Text: false
- Reviewed:
- Description: In this paper we present a dual criterion for the maximal monotonicity of the composition operator T:=A* SA, where S:Y→→ Y is a maximal monotone (set-valued) operator and A: X→ Y is a continuous linear map with the adjoint A*, X and Y are reflexive Banach spaces, and the product notation indicates composition. The dual criterion is expressed in terms of the closure condition involving the epigraph of the conjugate of Fitzpatrick function associated with S, and the operator A. As an easy application, a dual criterion for the maximality of the sum of two maximal monotone operators is also given. © 2006 Springer Science+Business Media B.V.
- Description: C1
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
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- 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
About subdifferential calculus for abstract convex functions
- Authors: Sharikov, Evgenii
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Nonlinear and Convex Analysis Vol. 8, no. 2 (2007), p. 257-275
- Full Text: false
- Reviewed:
- Description: We introduce a stronger version of the strong globalization property of Rolewicz and examine the corresponding subdifferential calculus for abstract convex functions. In particular, we calculate a formula for the abstract subdifferential of the maximum of a finite set of abstract convex functions. We also present some examples of families of functions, which possess this new strong globalization property.
- Description: C1
- Description: 2003005856
An open mapping theorem for pro-Lie groups
- Authors: Hofmann, Karl , Morris, Sidney
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of the Australian Mathematical Society Vol. 83, no. 1 (2007), p. 55-77
- Full Text: false
- Reviewed:
- Description: A pro-Lie group is a projective limit of finite dimensional Lie groups. It is proved that a surjective continuous group homomorphism between connected pro-Lie groups is open. In fact this remains true for almost connected pro-Lie groups where a topological group is called almost connected if the factor group modulo the identity component is compact. As consequences we get a Closed Graph Theorem and the validity of the Second Isomorphism Theorem for pro-Lie groups in the almost connected context. © 2007 Australian Mathematical Society.
- Description: C1
- Description: 2003005492
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
Convex along lines functions and abstract convexity. Part i
- Authors: Crespi, G. P. , Ginchev, I. , Rocca, M. , Rubinov, Alex
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Convex Analysis Vol. 14, no. 1 (2007), p. 185-204
- Full Text: false
- Reviewed:
- Description: The present paper investigates the property of a function f : Rn → R+∞ := R U {+∞} with f(0) < +∞ to be Ln-subdifferentiable or Hn-convex. The Ln-subdifferentiability and Hnn-convexity are introduced as in Rubinov [9]. Some refinements of these properties lead to the notions of Ln0-subdifferentiability and Hn0-convexity. Their relation to the convex-along (CAL) functions is underlined in the following theorem proved in the paper (Theorem 5.6): Let the function f : Rn → R+∞ be such that f(0) < +∞ and f is Hn-convex at the points at which it is infinite. Then if f is Ln0-subdifferentiable, it is CAL and globally calm at each x0 ∈ dom f. Here the notions of local and global calmness are introduced after Rockafellar, Wets [8] and play an important role in the considerations. The question is posed for the possible reversal of this result. In the case of a positively homogeneous (PH) and CAL function such a reversal is proved (Theorem 6.2). As an application conditions are obtained under which a CAL PH function is Hn0-convex (Theorems 6.3 and 6.4). © Heldermann Verlag.
- Description: C1
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
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- 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
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
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:
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- 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
On mixed Moore graphs
- Authors: Nguyen, Minh Hoang , Miller, Mirka , Gimbert, Joan
- Date: 2007
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 307, no. 7-8 (2007), p. 964-970
- Full Text: false
- Reviewed:
- Description: The Moore bound for a directed graph of maximum out-degree d and diameter k is M
- Description: C1
- Description: 2003005024