Root square mean labelling of some graphs obtained from path

Abstract

Let G be a graph with q edges. A labelling f of G is said to be root square mean labelling if f: V(G)UE(G)→{1,2,…,q+1} such that when each edge e = uv labelled with f(e)=[f(u)2+f(v)2/2] or f(e)=[f(u)2+f(v)2/2] then the resulting edge labels are distinct. A graph G is called a root square mean graph if G can be labelled by a root square mean labelling. In this paper we determine a root mean square labelling of two graphs obtained from path, which are corona product of ladder and complete graph with order 1, and a graph obtained from triangular snake by join one vertex with degree 2 in each triangle to a new vertex. The method of labelling construction is we need to do labeling to the vertices of the graph with label 1, 2, 3, …, q+1. The labels of the vertices are not necessarily different. The next step is we need to do labeling to the edges with the certain formula by using the vertex labeling. The edge labels must be different. By the labelling we construct, we proof that the two graphs are root square mean graphs.