For a simple graph G, a vertex labeling f: V (G) → (1; 2....,k) is called a k-labeling. The weight of a vertex v, denoted by wtf (v) is the sum of all vertex labels of vertices in the closed neighborhood of the vertex v. A vertex k-labeling is defined to be an inclusive distance vertex irregular distance k-labeling of G if for every two different vertices u and v there is wtf (u) ≠ wtf (v). The minimum k for which the graph G has a vertex irregular distance k-labeling is called the inclusive distance vertex irregularity strength of G. In this paper we establish a lower bound of the inclusive distance vertex irregularity strength for any graph and determine the exact value of this parameter for several families of graphs.
|Número de páginas
|Electronic Journal of Graph Theory and Applications
|Publicada - 2018
|Publicado de forma externa