Extremal values of vertex‐degree‐based topological indices of coronoid systems

Abstract

A vertex‐degree‐based (VDB for short) topological index φ induced by the numbers {φi,j}, is defined for a graph G with n vertices as φ()G=∑1≤i≤j≤n−1mi,jφi,j, where mi,j is the number of edges in G joining vertices of degree i and j. Our main concern is to study VDB topological indices over important classes of coronoid systems. Recall that a coronoid system is a natural representation of a coronoid hydrocarbon and can be defined as a benzenoid‐like system with a hole. In this paper we determine the extremal values of a VDB topological index φ over the set of primitive coronoid systems, the set of catacondensed coronoid systems, and the set of circumscribed coronoid systems.

Symmetric Division Deg Index: Extremal Results and Bounds

“…The descriptors of the form (1) are referred to as bond incident degree (BID) indices [80]; another often used name for such descriptors is vertexdegree-based (VDB) indices [17,21].…”

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

“…A coronoid system can be regarded as a benzenoid system that is allowed to have 'holes' such that the perimeter of the coronoid system and the perimeters of the holes are pairwise disjoint. There are many results on topological index of coronoid systems [33,34]. We now consider a special family of coronoid systems, denoted by K(n, p, r) (see Figure 6), which is formally generated from polycyclic benzenoid systems by circumcising some interior atoms or bonds.…”

“…A coronoid system can be regarded as a benzenoid system that is allowed to have ‘holes’ such that the perimeter of the coronoid system and the perimeters of the holes are pairwise disjoint. There are many results on topological index of coronoid systems [33, 34]. We now consider a special family of coronoid systems, denoted by K ( n , p , r ) (see Figure 6), which is formally generated from polycyclic benzenoid systems by circumcising some interior atoms or bonds.Theorem Let G be the K ( n , p , r ) coronoid structure with r ≥ 1, n ≥ 3 and 1 ≤ p ≤ n. Then Proof .…”

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

“…There are many results on topological index of coronoid systems [13,6]. We now consider a special family of coronoid systems, denoted by K(n, p, r) (see Figure 4), which is formally generated from polycyclic benzenoid systems by circumcising some interior atoms or bonds.…”