Total Labellings of Some Connected Graphs

Abstract

Ashraf et al. in [3] introduced the concept of vertex H irregular labelling and edge H irregular labelling. Let H be sub graph of given graph G. If each edge of graph G is contained in any subgraph Hi where i ={ 1,2,3,…, k } of G and if each Hi is isomorphic to given subgraph H. then the collection Hi of subgraphs of G is said to be H-covering of G. They also introduced the concept of edge H irregular strength ehs(G) that is the minimum k for which the graph has total H irregular k labelling and vertex H irregular strength vhs(G) that is the minimum k for which the graph has total H irregular k labelling The thesis is devoted to study the total vertex C3 irregular strength wheel graph and triangular ladder graph taking subgraph C3. We also found the total vertex C4 irregular strength ladder graph and grid graph. Furthermore, we find the total vertex C8 irregular strength of a connected graph Qn.