On Total Irregularity Strength of Double-Star and Related Graphs

Diari Indriati, Widodo, Indah Emilia Wijayanti, Kiki Ariyanti

Research output: Contribution to journalConference articlepeer-review

9 Citations (Scopus)

Abstract

Let G = (V, E) be a simple and undirected graph with a vertex set V and an edge set E. A totally 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 x1, their weights wtf(x) = f(x) + ∑xyεE f(xy) and wtf(x′) = f(x′) + ∑xyεE f(x′y′)are distinct, and for any two different edges xy and x1y1 their weights f (x) + f (xy) + f (y) and f (x1) + f (x1y1) + f (y1) are also distinct. A total irregularity strength of graph G, denoted byts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for double-star Sn,m, n, m ≥ 3 and graph related to it, that is a caterpillar Sn,2,n, n ≥ 3. The results are and ts(Sn,2,n) = [n+m-1/2] ts(Sn,2,n)n.

Original languageEnglish
Pages (from-to)118-123
Number of pages6
JournalProcedia Computer Science
Volume74
DOIs
Publication statusPublished - 1 Jan 2015
Event2nd International Conference of Graph Theory and Information Security, 2015 - Bandung, Indonesia
Duration: 21 Sep 201523 Sep 2015

Keywords

  • caterpillar
  • double-star
  • total irregularity strength
  • Totally irregular total k-labeling
  • weight

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