Open AccessЦветовая энергия некоторых кластерных графов
Author(s) -
Sabitha D’Souza,
Kulambi Parameshwarappa Girija,
H. J. Gowtham,
Pradeep G. Bhat
Publication year - 2021
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.46698/x5522-9720-4842-z
Subject(s) - combinatorics , triangle free graph , mathematics , bipartite graph , graph power , adjacency matrix , vertex (graph theory) , discrete mathematics , 1 planar graph , complete bipartite graph , edge coloring , chordal graph , line graph , graph
Let $G$ be a simple connected graph. The energy of a graph $G$ isdefined 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$\pi$-electron energy of a conjugated hydrocarbon as calculated by the Huckelmolecular orbital (HMO) method in quantum chemistry. A coloring of a graph $G$ isa 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 thechromatic number of $G$ and is denoted by $\chi(G)$. 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.