Displaying similar documents to “On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs”

Gallai and anti-Gallai graphs of a graph

Aparna Lakshmanan S., 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 H -free for any finite graph H . 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.

On total vertex irregularity strength of graphs

K. Muthu Guru Packiam, Kumarappan Kathiresan (2012)

Discussiones Mathematicae Graph Theory

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Martin Bača et al. [2] introduced the problem of determining the total vertex irregularity strengths of graphs. In this paper we discuss how the addition of new edge affect the total vertex irregularity strength.

γ-graphs of graphs

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)...

Extremely Irregular Graphs

M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, I. Gutman (2013)

Kragujevac Journal of Mathematics

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The Smallest Non-Autograph

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....