TY - JOUR

T1 - The reflexive vertex strength on cycle and generalized friendship graph

AU - Agustin, Ika Hesti

AU - Utoyo, M. Imam

AU - Dafik,

AU - Mohanapriya, N.

AU - Slamin,

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.

PY - 2023/8/1

Y1 - 2023/8/1

N2 - Let G be a simple, un-directed and connected graph. The graph G has a pair of sets (V (G),E(G)), where V (G) is nonempty vertex set and E(G) is an unordered pair of sets with two distinct vertices u,v in V (G). A total k-labeling is defined as a function fe from the edge set to a set {1, 2, 3,...,ke} and a function fv from the vertex set to a set {0, 2, 4,..., 2kv}, where k =max{ke, 2kv}. The total k-labeling is a vertex irregular reflexivek-labeling of the graph G, if for every two different vertices u and u′ of G, wt(u) wt(u′), where wt(u) = fv(u) + uv E(G)fe(uv). The reflexive vertex strength of the graph G, denoted by rvs(G) is the minimum k for graph G which has a vertex irregular reflexive k-labeling. In this paper, we determined the exact value of the reflexive vertex strength of cycle and generalized friendship graph.

AB - Let G be a simple, un-directed and connected graph. The graph G has a pair of sets (V (G),E(G)), where V (G) is nonempty vertex set and E(G) is an unordered pair of sets with two distinct vertices u,v in V (G). A total k-labeling is defined as a function fe from the edge set to a set {1, 2, 3,...,ke} and a function fv from the vertex set to a set {0, 2, 4,..., 2kv}, where k =max{ke, 2kv}. The total k-labeling is a vertex irregular reflexivek-labeling of the graph G, if for every two different vertices u and u′ of G, wt(u) wt(u′), where wt(u) = fv(u) + uv E(G)fe(uv). The reflexive vertex strength of the graph G, denoted by rvs(G) is the minimum k for graph G which has a vertex irregular reflexive k-labeling. In this paper, we determined the exact value of the reflexive vertex strength of cycle and generalized friendship graph.

KW - Reflexive vertex strength

KW - cycle graph

KW - generalized friendship graph

KW - vertex irregular reflexive labeling

UR - http://www.scopus.com/inward/record.url?scp=85154572751&partnerID=8YFLogxK

U2 - 10.1142/S1793557123501371

DO - 10.1142/S1793557123501371

M3 - Article

AN - SCOPUS:85154572751

SN - 1793-5571

VL - 16

JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

IS - 8

M1 - 2350137

ER -