Discrimination power of graph measures based on complex zeros of the partial Hosoya polynomial

Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix

“…The sizes of these classes are depicted in corresponding tables. As in [4], we generated the graphs by employing the package Nauty due to McKay [45] and implemented the graph measures M i , 1 ≤ i ≤ 3 in R.…”

“…It expresses the number of nondistinguishable values, i.e., the number of graphs that cannot be distinguished structurally by their descriptor values [4,39,46].…”

“…To do so, we use the basic form of the measures which have been recently defined by Dehmer et al [4]. In this paper, we demonstrate that these measures based on the zeros of the characteristic polynomial by using the Randić matrix [25][26][27][28] encode structural information more uniquely than by using the zeros of other graph polynomials.…”

“…Graph polynomials have been proven useful in several scientific disciplines, see, e.g., [1][2][3][4][5][6][7]. The purpose to use this concept can be multifaceted as the polynomials could be used, e.g., as counting polynomials or to characterize networks quantitatively based on their zeros.…”

“…The purpose to use this concept can be multifaceted as the polynomials could be used, e.g., as counting polynomials or to characterize networks quantitatively based on their zeros. A prominent example is the Hosoya polynomial [2,[8][9][10] whose zeros have been used to define topological indices [4,11]. Also, there exists the well-known Hosoya index [12,13] that is defined by the coefficient of the so-called matching polynomial [3].…”