TY - JOUR

T1 - On the Construction of the Reflexive Vertex k -Labeling of Any Graph with Pendant Vertex

AU - Agustin, I. H.

AU - Utoyo, M. I.

AU - Dafik,

AU - Venkatachalam, M.

AU - Surahmat,

N1 - Publisher Copyright:
© 2020 I. H. Agustin et al.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85093943048&partnerID=8YFLogxK

U2 - 10.1155/2020/7812812

DO - 10.1155/2020/7812812

M3 - Article

AN - SCOPUS:85093943048

SN - 0161-1712

VL - 2020

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

M1 - 7812812

ER -