Some properties on the lexicographic product of graphs obtained by monogenic semigroups


Akgunes N., Das K. C. , ÇEVİK A. S. , CANGÜL İ. N.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2013
  • Doi Number: 10.1186/1029-242x-2013-238
  • Title of Journal : JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Keywords: monogenic semigroup, lexicographic product, clique number, chromatic number, independence number, domination number, ZERO-DIVISOR GRAPH, RADIUS, NUMBER

Abstract

In (Das et al. in J. Inequal. Appl. 2013:44, 2013), a new graph Gamma (S-M) on monogenic semigroups S-M (with zero) having elements {0, x, x(2), x(3),..., x(n)} was recently defined. The vertices are the non-zero elements x, x(2), x(3),..., x(n) and, for 1 <= i, j <= n, any two distinct vertices x(i) and x(j) are adjacent if x(i)x(j) = 0 in S-M. As a continuing study, in an unpublished work, some well-known indices (first Zagreb index, second Zagreb index, Randic index, geometric-arithmetic index, atom-bond connectivity index, Wiener index, Harary index, first and second Zagreb eccentricity indices, eccentric connectivity index, the degree distance) over Gamma (S-M) were investigated by the same authors of this paper.