On the vertex irregular reflexive labeling of several regular and regular-like graphs. (4th July 2022) - Agustin, Ika H.; Susilowati, Liliek; Dafik,; Cangul, Ismail N.; Mohanapriya, N.
Abstract: A total k -labeling is defined as a function g from the edge set to the first natural number ke and a function f from the vertex set to a non-negative even number up to 2 kv, where k = max { ke, 2 kv }. A vertex irregular reflexive k-labeling of the graph G is total k -labeling if wt ( x ) ¹ wt ( x ¢) for every two different vertices x and x ¢ of G, where wt ( x ) = f ( x ) + Σ xy ∈ E ( G ) g ( xy ). The reflexive vertex strength of the graph G, denoted by rvs ( G ), is the minimum k for a graph G with a vertex irregular reflexive k -labeling. We will determine the exact value of rvs ( G ) in this paper, where G is a regular and regular-like graph. A regular graph is a graph where each vertex has the same number of neighbors. A regular graph with all vertices of degree r is called an r -regular graph or regular graph of degree r . A regular-like graphs is an almost regular graph that we develop in a new definition and we called it with ( s, r ) -almost regular graphs.