Tomás Vetrík (2008)
Discussiones Mathematicae Graph Theory
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We derive an upper bound on the number of vertices in graphs of diameter 3 and given degree arising from Abelian lifts of dipoles with loops and multiple edges.
Lynne L. Doty (2011)
Discussiones Mathematicae Graph Theory
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For the notion of neighbor-connectivity in graphs whenever a vertex is subverted the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighbor-connectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is bounded above by κ. Doty has sharpened that bound in abelian Cayley graphs to approximately...
Miller, Mirka, Širáň, Jozef (2005)
The Electronic Journal of Combinatorics [electronic only]
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Dragoš Cvetković, Tatjana Davidović (2011)
Zbornik Radova
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Gutman, I. (1996)
Publications de l'Institut Mathématique. Nouvelle Série
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Dragoš Cvetković, Tatjana Davidović (2009)
Zbornik Radova
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M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, I. Gutman (2013)
Kragujevac Journal of Mathematics
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Simic, Slobodan K. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Philip J. Pratt, Donald W. Vanderjagt (1977)
Colloquium Mathematicae
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Jaroslav Ivanco (2007)
Discussiones Mathematicae Graph Theory
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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.
Isaak, Garth, West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Gliviak, Ferdinand, Kyš, P. (1997)
Acta Mathematica Universitatis Comenianae. New Series
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H. S. Ramane, D. S. Revankar, I. Gutman, H. B. Walikar (2009)
Publications de l'Institut Mathématique
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Caro, Yair, West, Douglas B. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Gerd H. Fricke, Sandra M. Hedetniemi, Stephen T. Hedetniemi, Kevin R. Hutson (2011)
Discussiones Mathematicae Graph Theory
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A set S ⊆ V is a dominating set of a graph G = (V,E) if every vertex in V -S is adjacent to at least one vertex in S. The domination number γ(G) of G equals the minimum cardinality of a dominating set S in G; we say that such a set S is a γ-set. In this paper we consider the family of all γ-sets in a graph G and we define the γ-graph G(γ) = (V(γ), E(γ)) of G to be the graph whose vertices V(γ) correspond 1-to-1 with the γ-sets of G, and two γ-sets, say D₁ and D₂, are adjacent in E(γ)...
Juan Alberto Rodríguez-Velázquez, Erick David Rodríguez-Bazan, Alejandro Estrada-Moreno (2017)
Discussiones Mathematicae Graph Theory
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In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.
Benjamin S. Baumer, Yijin Wei, Gary S. Bloom (2016)
Discussiones Mathematicae Graph Theory
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Suppose that G is a simple, vertex-labeled graph and that S is a multiset. Then if there exists a one-to-one mapping between the elements of S and the vertices of G, such that edges in G exist if and only if the absolute difference of the corresponding vertex labels exist in S, then G is an autograph, and S is a signature for G. While it is known that many common families of graphs are autographs, and that infinitely many graphs are not autographs, a non-autograph has never been exhibited....