The Terminal Hosoya Polynomial of Some Families of Composite Graphs

Abstract

Let G be a connected graph and let Ω(G) be the set of pendent vertices of G. The terminal Hosoya polynomial of G is defined as TH(G,t)∶=∑x,y∈Ω(G):x≠ytdG(x,y), where dG(x,y) denotes the distance between the pendent vertices x and y. In this note paper we obtain closed formulae for the terminal Hosoya polynomial of rooted product graphs and corona product graphs.

Topological Indices of Antibiotic Drugs used in Pneumonia Treatment with their QSPR Analysis and M-polynomial

“…We present the many regression models with value of 𝑅 2 ≥ 0.8 for the physicochemical properties in terms of proposed indices. In Tables (4,6,8,10,12,14), the value of p is less than or equal to 0.001 (p < 0.05), indicating the significance of the results. Consider the following regression models to obtain the relationship between the degree based topological indices and the physicochemical properties of these drugs.…”

“…A graph polynomial is an algebraic object associated with a graph that is typically invariant under graph isomorphism. Many algebraic graph polynomials have been introduced in the past, including the Hosoya polynomial [14], the Forgotten polynomial [15], the Pi polynomial [16], the Schultz polynomial, the Modified Schultz polynomial [17], the Matching polynomial [18], the Tutte polynomial [19], and the M-Polynomial. Degree-based topological indices are particularly relevant in chemistry among these groups.…”

M-polynomial and topological indices of zigzag edge coronoid fused by starphene

“…A solid general technique that can generate topological indices of a specific class is that firstly compute the graph polynomial and then by taking the integral or a derivative or both of the graph polynomial at some specific point provided the topological descriptor. The procedure of this method is called the Hosoya polynomial [11]. This is the best knowing general graph polynomial in the perspective of resolving the topological descriptor that is dependent on the distance of vertices.…”

Computing the metric dimension of a graph from primary subgraphs

“…Moreover, this construction was used in [6] to study the terminal Hosoya polynomial of composite graphs and in [16] to compute the local metric dimension of graphs with cut vertices.…”