On the vertex irregular reflexive labeling of several regular and regular-like graphs

Ika H. Agustin, Liliek Susilowati, Dafik, Ismail N. Cangul, N. Mohanapriya

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 2kv, where k = max{ke, 2kv }. 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.

Original languageEnglish
Pages (from-to)1457-1473
Number of pages17
JournalJournal of Discrete Mathematical Sciences and Cryptography
Issue number5
Publication statusPublished - 2022


  • 05C78
  • Almost regular graph
  • Irregular reflexive k-labeling
  • Reflexive vertex strength
  • Regular graph
  • Regular-like graph


Dive into the research topics of 'On the vertex irregular reflexive labeling of several regular and regular-like graphs'. Together they form a unique fingerprint.

Cite this