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In this section, we present some new bounds for the first and second Zagreb indices of graphs and compare them with each other. Lemma 1. Let G be a graph. Then M 1 (G) 2M 2 (G) with equality if and only if G is an. empty graph or a complete graphs with two vertices. Lemma 2. Let G be a graph with. ( G ) 2 . Then M 1 (G) M 2 (G) with equality if and
In this paper, we have reported some properties, especially upper and lower bounds, for these two graph invariants of connected (molecular) graphs. Moreover, some correspond-ing extremal graphs have been characterized with respect to these two indices. Keywords: vertex degree, tree, upper or lower bound.
The modified first Zagreb connection index of a triangle-free and quadrangle-free graph G is equal to 2M2(G) M1(G), where M2(G) and M1(G) are the well-known second and first Zagreb indices of G, respectively.
In this paper we study the relations between the Zagreb indices and the modified Zagreb indices, and we present some bounds for the modified Zagreb indices. The Zagreb indices were introduced by Gutman and Trinajsti. d ( v ) are the degrees of vertices u and v respectively. For recent work on Zagreb indices see.
In this paper, we determine all relations between the Zagreb indices and coindices of a graph G and of its complement G. In Section 2 we focus our attention to the. rst Zagreb index, in Section 3 to the second Zagreb index, whereas in Section 4 we obtain relations for the Zagreb indices of certain derived graphs.
10 maj 2023 · The bond incident degree (BID) index of a graph $ G $ is defined as $ BID_{f}(G) = \sum_{uv\in E(G)}f(d(u), d(v)) $, where $ d(u) $ is the degree of a vertex $ u $ and $ f $ is a non-negative real …
Let G =(V,E) be a simple graph with n = |V| vertices and m = |E| edges. The first Zagreb index M1 and the second Zagreb index M2 of G are defined as follows: M1 = i∈V d2 i and M2 = (i,j)∈E didj, where d1,d2,...,dn are vertex degrees, while didj represents weight associated to the edge (i,j). The
