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...

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 maximum integer skew-symmetric flow problem (MSFP) generalizes both the maximum flow and maximum matching problems. It was introduced by Tutte [28] in terms of self-conjugate flows in antisymmetrical digraphs. He showed that for these objects there are natural analogs of classical theoretical results on usual network flows, such as the flow decomposition, augmenting path, and max-flow min-c...

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...

Eilers et al. have recently completed the geometric classification of unital graph $C^\ast$-algebras up to Morita equivalence using a set moves on corresponding digraphs. We explore question whether these preserve nonzero elements spectrum finite digraph, which in this paper is allowed loops and parallel edges. consider several different digraph spectra that been studied literature, answering f...

in this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. also, we represent several theorems for constructing each generalized skew t-normal distribution. next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, nickel and vanadium, associated with crude oil in shadgan wetland in the south-...

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...