Edge irregular reflexive labelling on corona of cycle and null graph

Abstract

Let G(V, E) be a simple and connected graph in which the set of vertices in V(G) and set of edges is E(G). Graph labeling is a mapping between the elements of a graph to a number (usually positive integer or non-negative integer). There are many kinds of graph labeling, one of them is edge irregular reflexive k-labeling. Edge irregular reflexive k-labeling δ on G(V, E) is an assignment that carries the numbers of integer to elements of graph, such that the positive integer {1, 2, 3, …, ke} assignment to edges of the graph and the even positive integer {0, 2, 4, …, 2kv} assignment to vertices of a graph. Reflexive edge strength of G(V, E) denoted as res(G), that is a minimum k that using for labeling δ on G(V, E). The corona of cycle and null graph denoted as Cp ⊙ Nq is a graph that formed by one copy of graph Cp and p-copy graph of Nq with i-th vertex from Cp is connected to all of vertices from i-th copy of graph Nq. This paper will discuss edge irregular reflexive k-labeling for the corona of the cycle and null graph number of vertices equal 1 and 2 (mod 6) and also their reflexive edge strengths.