Back to Search Start Over

The reflexive vertex strength on cycle and generalized friendship graph.

The reflexive vertex strength on cycle and generalized friendship graph.

Authors :
Agustin, Ika Hesti
Utoyo, M. Imam
Dafik
Mohanapriya, N.
Slamin
Source :
Asian-European Journal of Mathematics; Aug2023, Vol. 16 Issue 8, p1-19, 19p
Publication Year :
2023

Abstract

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 f e from the edge set to a set { 1 , 2 , 3 , ... , k e } and a function f v from the vertex set to a set { 0 , 2 , 4 , ... , 2 k v } , where k = max { k e , 2 k v }. The total k -labeling is a vertex irregular reflexive k -labeling of the graph G , if for every two different vertices u and u ′ of G , wt (u) ≠ wt (u ′) , where wt (u) = f v (u) + ∑ u v ∈ E (G) f e (u v). 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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
17935571
Volume :
16
Issue :
8
Database :
Complementary Index
Journal :
Asian-European Journal of Mathematics
Publication Type :
Academic Journal
Accession number :
169914102
Full Text :
https://doi.org/10.1142/S1793557123501371