On Degree Sequence of Total Graphs and the Order of the Graphs

On Degree Sequence of Total Graphs and the Order of the Graphs

In this dissertation we discuss about the degree sequence of total graphs of some general graphs. A total graph of G, denoted by T(G) has vertex set as the union of vertices and edges in G and vertices are adjacent in T(G) if they are adjacent or incident in G. We try to obtain the degree sequence of total graphs of particular graphs like complete graph, path, cycle, wheel and star, from the number of vertices of the given graph (without directly drawing the total graph). We also explain the decomposition of T(G) into G and K_(d_i )s where dis are degrees of each of the vertices in G, moreover discuss about the degree sequence of T(G)??T(Ge).

Thomas Jijo

Mathematics