The two Zagreb indices M 1=∑ vd (v) 2 and M 2=∑ uvd (u) d (v) are vertex-degree-based
graph invariants that have been introduced in the 1970s and extensively studied ever since …

For any real number α, the sum of the α-th powers of the degrees of a (molecular) graph G,
denoted by 0Rα (G), is known as the general zeroth–order Randic index as well as the …

Let\(G=(V, E)\) be a simple connected graph with vertex set\(V=\{1, 2,\ldots, n\}\) and edge
set\(E=\{e_1, e_2,\ldots, e_m\}\). Let\(d_i\) be the degree of its vertex\(i\) and\(d (e_i)\) the …

Two weighted inequalities for real non-negative sequences are proven. The first one
represents a generalization of the Szőkefalvi Nagy inequality for the variance, and the …

Abstract Let G=(V (G), E (G)) G=(V(G),E(G)) be a graph. A set D⊆ V (G) D⊆V(G) is a
distance k-dominating set of G if for every vertex u∈ V (G)∖ D u∈V(G)∖D, d G (u, v)≤ k …

REMARK ON FORGOTTEN TOPOLOGICAL INDEX OF A LINE GRAPHS Page 1 BULLETIN OF
THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) …

The edge version of traditional first Zagreb index is known as first reformulated Zagreb
index. In this paper, we analyze and compare various lower and upper bounds for the first …

Let G=(V, E), V={1, 2,..., n}, E={e1, e2,..., em}, be a simple graph with n vertices and m edges.
Denote by d1≥ d2≥...≥ dn> 0, and d (e1)≥ d (e2)≥ d (em), sequences of vertex and edge …

Let $ G $ be a graph with edge set $ E (G) $. The first and second reformulated Zagreb
indices of $ G $ are defined as $ E M_1 (G)=\sum_ {e\in E (G)}\operatorname {deg}(e)^ 2 …

A connected acyclic graph in which the degree of every vertex is at most four is called a
molecular tree. A number associated with a molecular tree that can help to approximate the …