Spectral Properties of Partial Chain and Partial Threshold Graphs

Chain graphs and threshold graphs play an important role in Spectral Graph Theory. Nesting in the neighborhood of vertices in these graphs has gained the attention of various researchers. Motivated by this structure, recently two new classes of graphs, namely partial chain graphs and partial threshold graphs have been defined. In this article, we give a few bounds on the spectral radius and energy of partial chain graphs and partial threshold graphs in terms of the total number of vertices. We obtained a class of partial chain graphs and partial threshold graphs with exactly two main eigenvalues. The energy of some classes of partial threshold graphs and partial chain graphs are obtained.