On geometric mean graphs

Abstract

A Graph G=(V,E) with p vertices and q edges is said to be a Geometric mean if it is possible to label the vertices xv with distinct labels f(x) from 1,2,….q+1 in such a way that when each edge e=uv is labeled with f(e=uv) = ⌈√ () ()⌉ or ⌊√ () () ⌋, then the resulting edge labels are distinct. In this case f is called Geometric mean labeling of G. In this paper we investigate the Geometric mean labeling behavior for some new families of Graphs.

On b-coloring of central graph of some graphs

“…A Triangular Snake [8] is obtained from a path x 1 ; x 2 ; : : : ; x n by joining x i and x i+1 to a new vertex y i for 1 i n. That is, every edge of a path is replaced by a triangle C 3 . The n-Sunlet graph S n is a graph [11] with cycle C n and each vertex of the cycle attached to one pendent vertex.…”

$k$-geometric graphs

“…Geometric mean labeling was first introduced by Somasundaram et al (2011) in [2]. Many classes of geometric mean graphs are studied in [2], [3], [4], [5], [6], and [7]. Durai Baskar and Arockiaraj give a nice motivation and introduce the concept of F −geometric mean labeling, where only the flooring function is used, in [1].…”