On the Construction of the Reflexive Vertex k-Labeling of Any Graph with Pendant Vertex

Autor: I. H. Agustin, M. I. Utoyo, Dafik, M. Venkatachalam, Surahmat
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2020 (2020)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
DOI: 10.1155/2020/7812812
Popis: A total k-labeling is a function fe from the edge set to first natural number ke and a function fv from the vertex set to non negative even number up to 2kv, where k=maxke,2kv. A vertex irregular reflexivek-labeling of a simple, undirected, and finite graph G is total k-labeling, if for every two different vertices x and x′ of G, wtx≠wtx′, where wtx=fvx+Σxy∈EGfexy. The minimum k for graph G which has a vertex irregular reflexive k-labeling is called the reflexive vertex strength of the graph G, denoted by rvsG. In this paper, we determined the exact value of the reflexive vertex strength of any graph with pendant vertex which is useful to analyse the reflexive vertex strength on sunlet graph, helm graph, subdivided star graph, and broom graph.
Databáze: Directory of Open Access Journals
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