On inclusive distance vertex irregular labelings

Martin Baca, Andrea Semanicova-Fenovcikova, S. Slamin, Kiki A. Sugeng

Abstract


For a simple graph G, a vertex labeling f:V(G)\to {1, 2, ..., k} is called a  k-labeling. The weight of a vertex v, denoted by $wt_f(v)$ 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 $wt_f(u)\ne wt_f(v)$. 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.


Keywords


inclusive distance vertex irregular labeling, inclusive distance vertex irregularity strength

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DOI: http://dx.doi.org/10.5614/ejgta.2018.6.1.5

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ISSN: 2338-2287

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