The ISI-energy εisi(G) of a graph G=(V,E) is the sum absolute values eigenvalues ISI-matrix C(G)=[cij]n×n in which cij=d(vi)d(vj)d(vi)+d(vj) if vivj∈E(G) and cij=0 otherwise. d(vi) denotes degree vertex vi∈V. As class energy, can be utilized to ascertain general energy conjugated carbon molecules. Two non-isomorphic graphs same order are said ISI-equienergetic their ISI-energies equal. In this ...

The energy, E(G), of a simple graph G is defined to be the sum of the absolute values of the eigen values of G. If G is a k-regular graph on n vertices,then E(G) k+√k(n− 1)(n− k)= B2 and this bound is sharp. It is shown that for each > 0, there exist infinitely many n for each of which there exists a k-regular graph G of order n with k < n− 1 and B2 < . Two graphs with the same number of vertic...

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

For a graph G with vertex set V(G) = {v1, v2, . . . , vn}, the extended double cover G∗ is a bipartite graph with bipartition (X, Y), X = {x1, x2, . . . , xn} and Y = {y1, y2, . . . , yn}, where two vertices xi and yj are adjacent if and only if i = j or vi adjacent to vj in G. The double graphD[G] of G is a graph obtained by taking two copies of G and joining each vertex in one copy with the n...

In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, first the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of ...