The spectral polynomials of two joining graphs: splices and links

Energy of a graph, firstly defined by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix, in other words the sum of absolute values of the roots of the characteristic (spectral) polynomials, is an important sub area of graph theory. Symmetry and regularity are two important and desired properties in many areas including graphs. In many molecular graphs, we have a pointwise symmetry, that is the graph corresponding to the molecule under investigation has two identical subgraphs which are symmetrical at a vertex. Therefore, in this paper, we shall study only the vertex joining graphsIn this article we study the characteristic polynomials of the two kinds of joining graphs called splice and link graphs of some well known graph classes.