Rismawati Ramdani
Department Of Mathematics, Faculty Of Sciences And Technologies, Universitas Islam Negeri Sunan Gunung Djati, Jalan A.H. Nasution No. 105,

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Journal : Indonesian Journal of Combinatorics

On the total vertex irregularity strength of comb product of two cycles and two stars Rismawati Ramdani
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (323.824 KB) | DOI: 10.19184/ijc.2019.3.2.2

Abstract

Let G = (V(G),E(G)) be a graph and k be a positive integer. A total k-labeling of G is a map f : V ∪ E → {1,2,3,...,k}. The vertex weight v under the labeling f is denoted by w_f(v) and defined by w_f(v) = f(v) + \sum_{uv \in{E(G)}} {f(uv)}. A total k-labeling of G is called vertex irregular if there are no two vertices with the same weight. The total vertex irregularity strength of G, denoted by tvs(G), is the minimum k such that G has a vertex irregular total k-labeling. This labelings were introduced by Baca, Jendrol, Miller, and Ryan in 2007. Let G and H be two connected graphs. Let o be a vertex of H. The comb product between G and H, denoted by G \rhd_o H, is a graph obtained by taking one copy of G and |V(G)| copies of H and grafting the i-th copy of H at the vertex o to the i-th vertex of G. In this paper, we determine the total vertex irregularity strength of comb product of two cycles and two stars.