TOTAL VERTEX IRREGULARITY STRENGTH FOR THE AMALGAMATION PRODUCT OF PRISM AND TRIANGLE GRAPH
Susilawati, Syahidah, G. H. Putri, R. Kurnia, N. G. Tampubolon, A. Rahman

Faculty of Mathematics and Natural Sciences, Universitas Riau, Jalan H. R. Soebrantas, Kel. Simpang Baru, Kec.Tampan, Pekanbaru

Abstract

Let G=(V(G),E(G)) be a graph and k be a positive integer. A k-total labeling of G is a function f:V(G)&#8746-E(G)&#8594-{1,2,...,k}. Based on the labeling f, the weight of a vertex v is denoted by wf(v), where wf(v)=f(v)+&#8721-&#9618-&#12310-f(uv)&#12311- for uv&#8712-E(G). A k-total labeling of G is called a vertex irregular total k-labeling if no two distinct vertices have the same weight. The total vertex irregularity strength of G, denoted by tvs(G), is the smallest value of k such that G has a vertex irregular total k-labeling. Consider the graphs G and H, with orders n and m, respectively. The amalgamation of Amal (G,H) is a graph that formed by taking one copy of G and n copy of H, and merging one vertex from each graph G and H in each i-th copy for 1&#8804-i&#8804-n. In this paper we studies about total vertex irregularity strength for the amalgamation product of prism and triangle graph Amal(P_2 &#12310-&#9633-C&#12311-_n,C_3 ). The result show that tvs(Amal(P_2&#9633-&#9633-(C_n ),C_3 ))=&#8968-(4n+2)/3&#8969-.

Keywords: Vertex irregularity strength, labelling graph, amalgamation

Topic: Mathematics