Some More Results on Root Square Mean Graphs

S S Sandhya,S Anusa,S Somasundaram

doi:10.5539/jmr.v1n1p72

Abstract

A graph with vertices and edges is called a Root Square Mean graph if it is possible to label the vertices with distinct elements from in such a way that when each edge is labeled with or , then the resulting edge labels are distinct. In this case is called a Root Square Mean labeling of . The concept of Root Square Mean labeling was introduced by (S. S. Sandhya, S. Somasundaram and S. Anusa). We investigated the Root Square Mean labeling of several standard graphs such as Path, Cycle, Comb, Ladder, Triangular snake, Quadrilateral snake etc., In this paper, we investigate the Root Square Mean labeling for Double Triangular snake, Alternate Double Triangular snake, Double Quadrilateral snake, Alternate Double Quadrilateral snake, and Polygonal chain.

Highlights

The graph considered here will be finite, undirected and simple
A graph G = (V, E) with p vertices and q edges is called a Root Square Mean graph if it is possible to label the vertices x ∈ V with distinct elements f(x) from 1,2, ... , q + 1 in such a way that when each edge e = uv is labeled with f(e = uv) = ⌈√f(u)2+f(v)2 ⌉ or ⌊√f(u)2+f(v)2 ⌋, the resulting edge labels are distinct
We investigated the Root Square Mean labeling of several standard graphs such as Path, Cycle, Comb, Ladder, Triangular snake, Quadrilateral snake etc., In this paper, we investigate the Root Square Mean labeling for Double Triangular snake, Alternate Double Triangular snake, Double Quadrilateral snake, Alternate Double Quadrilateral snake, and Polygonal chain

Summary

Introduction

The graph considered here will be finite, undirected and simple. The vertex set is denoted by V(G) and the edge set is denoted by E(G).For all detailed survey of graph labeling we refer to Gallian (2010). A graph G = (V, E) with p vertices and q edges is called a Root Square Mean graph if it is possible to label the vertices x ∈ V with distinct elements f(x) from 1,2, ... Un by joining ui and ui+1 (Alternatively) to new vertices vi and wi respectively and joining vi and wi.An Alternate Double Quadrilateral snake A(D(Qn)) consists of two Alternate Quadrilateral snakes that have a common path.A Polygonal chain Gm,n is a connected graph all of whose m blocks are polygons on n sides.

Results

Conclusion