The total vertex irregularity strength of generalized helm graphs and prisms with outer pendant edges

Diari Indriati, Widodo, Indah E. Wijayanti, Kiki Ariyanti, Martin Bača, Andrea Semaničová-Feňovčíková

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

For a simple graph G = (V,E) with the vertex set V and the edge set E, a vertex irregular total k-labeling f: V ∪E → {1, 2,…, k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x′, their weights wtf (x) = f(x) + ∑xy ∈E f(xy) and wtf (x′) = f(x′)+ ∑x ′y ∈E f(x′y′) are distinct. A smallest positive integer k for which G admits a vertex irregular total k-labeling is defined as a total vertex irregularity strength of graph G, denoted by tvs(G). In this paper, we determine the exact value of the total vertex irregularity strength for generalized helm graphs and for prisms with outer pendant edges.

Original languageEnglish
Pages (from-to)14-26
Number of pages13
JournalAustralasian Journal of Combinatorics
Volume65
Issue number1
Publication statusPublished - 1 Jan 2016

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