On the total vertex irregularity strength of Cn *2 Kn graph
I K Dewi, Diari Indriati, Tri Atmojo Kusmayadı · Journal of Physics Conference Series · 2019
Let G be a connected and undirected graph with vertex set V ( G ) and edge set E ( G ). A vertex irregular total k -labeling of a graph is an assignment of positive integers set {1, 2, 3, ... k } so that the weight for all vertices are distinct. The weight of vertex u in G , denoted by wt ( u ), is defined as the sum of the label of vertex u and the label of all edges incident with vertex u . Total vertex irregularity strength of G , denoted by tvs ( G ), is the minimum value of the largest label k over all such vertex irregular total k -labelings. The C n * 2 K n graph is a graph obtained by edge operation amalgamation of cycle graph C n with complete graph K n . In this paper, we investigate the total vertex irregularity strength of C n * 2 K n graphs, for n ≥ 3. The result is for n ≥ 3, 4 and for n ≥ 5