Physical and functional constraints on biological networks lead to complex topological
patterns across multiple scales in their organization. A particular type of higher-order …

Various distance-based root-indices of graphs are introduced and studied in the present
article. They are obtained as unique positive roots of modified graph polynomials. In …

A huge number of topological graph measures have been defined and investigated. It turned
out that various graph measures failed to solve problems meaningfully in the context of …

We propose an asymmetry index as a measure of degree of asymmetry of a given dataset. It
provides an additional information on a dataset allowing to guide and improve any further …

For a graph G with orbits O 1,…, O k, the orbit polynomial is defined as OG (x)=∑ i= 1 kx| O
i|. In the current work, we will characterize all fullerenes concerning their pentagonal orbit …

In this paper, we examine roots of graph polynomials where those roots can be considered
as structural graph measures. More precisely, we prove analytical results for the roots of …

This work brings applications of the Lambert-Tsallis W q function in graph theory and
quantum networks. Initially, the function W q is used to represent the k colorings of certain …

In this article, we introduce a new counting polynomial, namely the orbit polynomial. It is well-
known that this polynomial has a unique positive zero δ in the interval [0, 1]. The aim of this …

In this paper, we define novel graph measures for directed networks. The measures are
based on graph polynomials utilizing the out-and in-degrees of directed graphs. Based on …

This paper addresses the problem of comparing different measures of graph symmetry. Two
measures, each based on the number and respective sizes of the vertex orbits of the …