ON TOTAL EDGE IRREGULAR STRENGTH OF TRIANGLE RELATED GRAPHS

Abstract

An edge irregular total h -labeling of a simple, undirected and connected graph G(V,E) is a labeling defined by H : V ∪E → {1,2,3,...,h} so that for any two distinct edges pq,rs their weights are different; i.e. W_H (pq) 6 \ne W_H (rs) where W_H (pq) = H(p)+H(q)+H(pq). A total edge irregular strength [TEIS] of a graph G, denoted by tes(G), is a labelling with the minimum h. In this paper, we have calculated the exact value of TEIS of triangle related graphs namely half gear graph, double fan graph and triangular snake graph.