论文标题
在具有给定连接性的两分图的最大Zagreb索引上
On the maximum Zagreb indices of bipartite graphs with given connectivity
论文作者
论文摘要
图的第一个Zagreb索引$ m_ {1} $定义为每个顶点度的平方的总和，而图的第二个Zagreb索引$ m_ {2} $定义为每对相邻顶点的顶点乘积的总和。在本文中，我们研究了$κ$（g）= k $（$κ'（g）= s $）的两部分图的Zagreb索引，并获得了$ m_1（g）$和$ m_2（g）和$ m_2（g）$ g \ in \ mathcal in \ nathcal {v} $ n $ n pess，n $ g \ n qus）的上限。 $ \ MATHCAL {V}^k_n $是$κ$的两部分图，带有$κ（g）= k $，而$ \ Mathcal {e}^s_n $是$κ'（g）= s $的订单$ n $的订单$ n $的两位图。
The first Zagreb index $M_{1}$ of a graph is defined as the sum of the square of every vertex degree, and the second Zagreb index $M_{2}$ of a graph is defined as the sum of the product of vertex degrees of each pair of adjacent vertices. In this paper, we study the Zagreb indices of bipartite graphs of order $n$ with $κ(G)=k$ (resp. $κ'(G)=s$) and sharp upper bounds are obtained for $M_1(G)$ and $M_2(G)$ for $G\in \mathcal{V}^k_n$ (resp. $\mathcal{E}^s_n$), where $\mathcal{V}^k_n$ is the set of bipartite graphs of order $n$ with $κ(G)=k$, and $\mathcal{E}^s_n$ is the set of bipartite graphs of order $n$ with $κ'(G)=s$.
