Sharp bounds for the first Zagreb index and first Zagreb coindex
نویسندگان
چکیده
منابع مشابه
Bounds on First Reformulated Zagreb Index of Graph
The first reformulated Zagreb index $EM_1(G)$ of a simple graph $G$ is defined as the sum of the terms $(d_u+d_v-2)^2$ over all edges $uv$ of $G .$ In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.
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The first variable Zagreb index of graph $G$ is defined as begin{eqnarray*} M_{1,lambda}(G)=sum_{vin V(G)}d(v)^{2lambda}, end{eqnarray*} where $lambda$ is a real number and $d(v)$ is the degree of vertex $v$. In this paper, some upper and lower bounds for the distribution function and expected value of this index in random increasing trees (rec...
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Let $G=(V,E)$, $V={v_1,v_2,ldots,v_n}$, be a simple graph with$n$ vertices, $m$ edges and a sequence of vertex degrees$Delta=d_1ge d_2ge cdots ge d_n=delta$, $d_i=d(v_i)$. Ifvertices $v_i$ and $v_j$ are adjacent in $G$, it is denoted as $isim j$, otherwise, we write $insim j$. The first Zagreb index isvertex-degree-based graph invariant defined as$M_1(G)=sum_{i=1}^nd_i^2$, whereas the first Zag...
متن کاملOn the Bounds of the First Reformulated Zagreb Index
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 reformulated Zagreb index and we propose new lower and upper bounds which are stronger than the existing and recent results [Appl. Math. Comp. 273 (2016) 16-20]. In addition, we prove that our bounds are superior in co...
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2015
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2015.1274