On inclusive distance vertex irregularity strength of small identical copies of star graphs

Abstract

For a simple graph G, an inclusive distance vertex irregular k-labeling of G is a mapping λ : V (G) → {1, 2, . . . , k} such that all the vertex-weights are pairwise distinct, where the weight of a vertex v, denoted by wt(v), is the sum of labels of vertices in the close neighborhood of the vertex v. The minimum k for which the graph G has an inclusive distance vertex irregular k-labeling is called the inclusive distance vertex irregularity strength of G, dis( c G). Here we introduce a new lower bound for dis( c G) and determine the exact value of the inclusive distance vertex irregularity strength for identical copies of star graphs, especially 2Sn and 3Sn.