The neighbor expanded sum distinguishing index of Halin graphs

Jingjing Huo, Wai Chee SHIU*, Weifan Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let G = (V, E) be a graph. A total k-weighting c of G is a function c: V(G) ∪ E(G) → {1,2,...,k}. For x ∈ V(G), define w(x) = Σ(c(xy)+c(y)). A total k-weighting c of G is called neighbor expanded sum distinguishing (nesd for short) if w(u) ≠ w(v) for every uv ∈ E(G). The smallest value of k for which such a nesd total k-weighting of G exists is called the neighbor expanded sum distinguishing index of G, denoted by nesdt(G). In this paper, we prove that nesdt(G) ≤ 3 for any Halin graph G. Furthermore, nesdt(G) = 2 for the cubic Halin graphs G.

Original languageEnglish
Pages (from-to)63-73
Number of pages11
JournalArs Combinatoria
Volume141
Publication statusPublished - Oct 2018

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Halin graphs
  • Neighbor expanded sum distinguishing index
  • Total weighting

Fingerprint

Dive into the research topics of 'The neighbor expanded sum distinguishing index of Halin graphs'. Together they form a unique fingerprint.

Cite this