Total Vertex Irregularity Strength Of Equitable Complete M-partite Graphs

For a simple undirected graph G with vertex set V and edge set E,a total k-labeling λ:V∪E →{1,2,· · ·,k} is called a vertex irregular total k-labeling of G if for every two distinct vertices x and y of G their weights wt(x)and wt(y)are distinct where the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x.The total vertex irregularity strength of G,denoted by tvs(G),is the minimum k for which the graph G has a vertex irregular total k-labeling.The complete m-partite graph on n vertices in which each part has either[n/m]or[n/m]vertices is denoted by Tm,n.The total vertex irregularity strength of several equitable complete m-partite graphs,namely,T7,n,T8,n and T9,n are discussed in Chapter 2.In the third chapter,we present three conjectures.