Quotient Labeling of Corona of Ladder Graphs

Abstract

Let G (V, E) be a finite, non-trivial, simple and undirected graph of order n and size m. For an one to one assignment f: V(G)→{1,2,…., n}, A Quotient labeling f* : ???? ???? → {1, 2, ..... , n} defined by ???? ∗ (uv)=       ( ) ( ) f v f u where f(u) > f(v), then the edge labels need not be distinct. The q-labeling number ql(f*) is the maximum value of f*(E(G)), and the Quotient Labeling Number QL(G) is the minimum amongql(f*). The bounds for the Quotient labeling number for corona ofsome ladder graphs likeclosed ladder,open ladder, slanting ladder, open triangular ladder, closed triangular ladder and diagonal ladder are found in this paper.