ON THE TOTAL EDGE IRREGULARITY STRENGTH OF MODULAR PRODUCT OF P_3 AND P_n Mohamad Fahruli Wahyujati (1,a), M. Salman A. N (2,b), Alfiatri Arif Susilo (2,c).
(1) Mathematics Department Universitas Gadjah Mada, Yogyakarta Indonesia.
(2) Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa No. 10 Bandung 40132, Indonesia.
a) fahruliwahyujati[at]gmail.com
b) Corresponding author: msalman[at]math.itb.ac.id
c) alfiatrias[at]students.itb.ac.id
Abstract
For any simple indirected graph G=(V(G),E(G)), a labeling \alpha: V(G) \cup E(G) \longrightarrow \{1,2,\ldots,k\} is called an edge-irregular total k-labeling of G if every two distinct edges x_1x_2 and y_1y_2 in E(G) their weights are different. The weight of edge is denoted by w_\alpha(x_1x_2), where w_\alpha(x_1x_2)=\alpha(x_1)+\alpha(x_1x_2)+\alpha(x_2). The minimum k for which a graph G has an edge-irregular total k-labeling is called the total edge irregularity strength of G and is denoted by tes(G). In this paper, we determine the total edge-irregular strength of modular product of P_3 and P_n, where P_n is path graph on n vertices.
Keywords: Total edge-irregular strength, modular product graph, path
