On the Connectivities of the Generalized Line, Middle and Total Graph

Abstract

We investigate the generalized line graph, total graph and middle graph of the given graphs. First, replace a given graph G with a multigraph M having the same point set as G, then it constructs the total graph T(G) from G. Two suitable subgraphs M_x(G), L_x(G), of T_x(G) are considered as extensions of middle graph M(G) and line graph L(G) respectively.
We also consider the connectivities of graphs which are obtained as a special case of L_x(G), M_x(G) and T_x(G). Then we get some extensions of established theorems.