TY - JOUR

T1 - ЦВЕТОВАЯ ЭНЕРГИЯ НЕКОТОРЫХ КЛАСТЕРНЫХ ГРАФОВ

AU - D’Souza, Sabitha

AU - Girija, Kulambi Parameshwarappa

AU - Gowtham, Halgar Jagadeesh

AU - Bhat, Pradeep Ganapati

N1 - Publisher Copyright:
© 2021 D’Souza, S., Girija, K. P., Gowtham, H. J. and Bhat, P. G.

PY - 2021

Y1 - 2021

N2 - Let G be a simple connected graph. The energy of a graph G is defined as sum of the absolute eigenvalues of an adjacency matrix of the graph G. It represents a proper generalization of a formula valid for the total π-electron energy of a conjugated hydrocarbon as calculated by the Huckel molecular orbital (HMO) method in quantum chemistry. A coloring of a graph G is a coloring of its vertices such that no two adjacent vertices share the same color. The minimum number of colors needed for the coloring of a graph G is called the chromatic number of G and is denoted by χ(G). The color energy of a graph G is defined as the sum of absolute values of the color eigenvalues of G. The graphs with large number of edges are referred as cluster graphs. Cluster graphs are graphs obtained from complete graphs by deleting few edges according to some criteria. It can be obtained on deleting some edges incident on a vertex, deletion of independent edges/triangles/cliques/path P3 etc. Bipartite cluster graphs are obtained by deleting few edges from complete bipartite graphs according to some rule. In this paper, the color energy of cluster graphs and bipartite cluster graphs are studied.

AB - Let G be a simple connected graph. The energy of a graph G is defined as sum of the absolute eigenvalues of an adjacency matrix of the graph G. It represents a proper generalization of a formula valid for the total π-electron energy of a conjugated hydrocarbon as calculated by the Huckel molecular orbital (HMO) method in quantum chemistry. A coloring of a graph G is a coloring of its vertices such that no two adjacent vertices share the same color. The minimum number of colors needed for the coloring of a graph G is called the chromatic number of G and is denoted by χ(G). The color energy of a graph G is defined as the sum of absolute values of the color eigenvalues of G. The graphs with large number of edges are referred as cluster graphs. Cluster graphs are graphs obtained from complete graphs by deleting few edges according to some criteria. It can be obtained on deleting some edges incident on a vertex, deletion of independent edges/triangles/cliques/path P3 etc. Bipartite cluster graphs are obtained by deleting few edges from complete bipartite graphs according to some rule. In this paper, the color energy of cluster graphs and bipartite cluster graphs are studied.

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U2 - 10.46698/X5522-9720-4842-Z

DO - 10.46698/X5522-9720-4842-Z

M3 - Article

AN - SCOPUS:85109971693

SN - 1683-3414

SP - 54

EP - 64

JO - Vladikavkaz Mathematical Journal

JF - Vladikavkaz Mathematical Journal

IS - 2

ER -