A tree in which no vertex has a degree greater than 4 is called a chemical tree. The bond
incident degree index of a chemical tree T is defined as∑ xy∈ ET φ (deg T (x), deg T (y)) …

This article gives bounds on a substantial number of BID (bond incident degree) indices for
connected graphs in terms of their order, size, and maximum degree. The considered BID …

Guar gum is a non-ionic polysaccharide found in abundance in nature. It may be used as a
thickening agent, stabilizer, or emulsifier in pharmaceutical formulations, food products, or …

Consider a unicyclic graph G with edge set E (G). Let f be a real-valued symmetric function
defined on the Cartesian square of the set of all distinct elements of G's degree sequence. A …

Let G be a simple graph with vertex set\(V=\{v_ {1}, v_ {2},\ldots, v_ {n}\}\). The notion\(i\sim j\)
is used to indicate that the vertices\(v_ {i}\) and\(v_ {j}\) of G are adjacent. For a vertex\(v …

A connected graph with p vertices and q edges satisfying q= p+ 1 is referred to as a bicyclic
graph. This paper is concerned with an optimal study of the BID (bond incident degree) …

The use of graph theory in the fields of chemistry, pharmacy, communication, maps, and
aeronautics is significant. In order to study the properties of chemical compounds, the …

The degree of a vertex u in a graph G is denoted by dG (u). The symmetric division deg
(SDD) index of G is denoted by SDD (G) and is defined as SDD (G)=∑ xy∈ E (G)[dG (x)/dG …