Some results on super edge-magic deficiency of graphs

M. Imran, A. Q. Baig, A. S. Fenovcíková

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

An edge-magic total labeling of a graph G is a bijection f: V (G) ∪ E(G) → [1, 2,..., V (G) + E(G)], where there exists a constant k such that f(u) + f(uv) + f(v) = k, for every edge uv ∈ E(G). Moreover, if the vertices are labeled with the numbers 1, 2,..., V (G) such a labeling is called a super edge-magic total labeling. The super edge-magic deficiency of a graph G, denoted by μs(G), is the minimum nonnegative integer n such that G ∪ nK1 has a super edge-magic total labeling or is defined to be ∞ if there exists no such n. In this paper we study the super edge-magic deficiencies of two types of snake graph and a prism graph Dn for n ≡ 0 (mod 4). We also give an exact value of super edge-magic deficiency for a ladder Pn x K2 with 1 pendant edge attached at each vertex of the ladder, for n odd, and an exact value of super edge-magic deficiency for a square of a path Pn for n ≥ 3.

Original languageEnglish
Pages (from-to)237-249
Number of pages13
JournalKragujevac Journal of Mathematics
Volume44
Issue number2
Publication statusPublished - 2020

Keywords

  • Block graph
  • Corona of graphs
  • Prism
  • Snake graph
  • Square of graph
  • Super edge-magic deficiency
  • Super edge-magic total labeling

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'Some results on super edge-magic deficiency of graphs'. Together they form a unique fingerprint.

Cite this