The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.

We present HyperGraphDB, a novel graph database based on generalized hypergraphs where hyperedges can contain other hyperedges. This generalization automatically reifies every entity expressed in the database thus removing many of the usual difficulties in dealing with higher-order relationships. An open two-layered architecture of the data organization yields a highly customizable system where...

A vertex (edge) irregular total k-labeling ? of a graph G is labeling the vertices and edges with labels from set {1,2,...,k} in such way that any two different (edges) have distinct weights. Here, weight x sum label all incident x, whereas an edge to edge. The minimum k for which has called irregularity strength G. In this paper, we are dealing infinite classes convex polytopes generated by pr...

The Wiener index, W , is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of ∆ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown that generalized stars having the prope...

We launch the new probabilistic model checker Storm. It features the analysis of discreteand continuous-time variants of both Markov chains and MDPs. It supports the Prism and JANI modeling languages, probabilistic programs, dynamic fault trees and generalized stochastic Petri nets. It has a modular set-up in which solvers and symbolic engines can easily be exchanged. It offers a Python API for...