On independent vertices and edges of belt graphs.
Gutman, I. (1996)
Publications de l'Institut Mathématique. Nouvelle Série
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Gutman, I. (1996)
Publications de l'Institut Mathématique. Nouvelle Série
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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.
Juraj Bosák (1984)
Mathematica Slovaca
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Simic, Slobodan K. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Bagga, Jay (2004)
International Journal of Mathematics and Mathematical Sciences
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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....
Gary Chartrand, Farrokh Saba, Hung Bin Zou (1985)
Časopis pro pěstování matematiky
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Allan Bickle (2013)
Mathematica Bohemica
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The -core of a graph , , is the maximal induced subgraph such that , if it exists. For , the -shell of a graph is the subgraph of induced by the edges contained in the -core and not contained in the -core. The core number of a vertex is the largest value for such that , and the maximum core number of a graph, , is the maximum of the core numbers of the vertices of . A graph is -monocore if . This paper discusses some basic results on the structure of -cores and...