On a conjecture on the diameter of line graphs of graphs of diameter two
Harishchandra S. Ramane, Asha B. Ganagi, Ivan Gutman (2012)
Kragujevac Journal of Mathematics
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Harishchandra S. Ramane, Asha B. Ganagi, Ivan Gutman (2012)
Kragujevac Journal of Mathematics
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Ivan Gutman, Yeong Nan Yeh (1995)
Mathematica Slovaca
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S. Aparna Lakshmanan, S. B. Rao, A. Vijayakumar (2007)
Mathematica Bohemica
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The paper deals with graph operators—the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be -free for any finite graph . The case of complement reducible graphs—cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.
Halina Bielak (1983)
Časopis pro pěstování matematiky
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Bohdan Zelinka (1993)
Mathematica Bohemica
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The paper studies graphs in which each pair of vertices has exactly two common neighbours. It disproves a conjectury by P. Hliněný concerning these graphs.
Torgašev, Aleksandar (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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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)...