论文标题
在连接（n，m）的顶点级函数索引上最多四个
On the Vertex-Degree-Function Indices of Connected (n,m)-Graphs of Maximum Degree at Most Four
论文作者
论文摘要
考虑图$ g $和在$ g $的学位集上定义的实价$ f $。 $ g $的所有顶点$ v \ in v（g）$ g $的输出$ f（d_v）$的总和通常称为顶点数量 - 函数函数索引，并由$ h_f（g）$表示，其中$ d_v $代表$ g $ $ g $的V $ v $ v $的程度。本文在连接$ g $时，在订单和$ g $的索引$ h_f（g）$上给出了尖锐的界限，最高学位最高$ 4 $。所有实现派生界限的图形都均应确定。涉及几个现有索引的界限 - 包括一般的Zeroth -rorderrandić索引和CoIndex，一般乘法第一/第二个Zagreb索引，变量总和LODEG索引和变量总和EXDEG索引 - 被推荐为已获得的特殊情况。
Consider a graph $G$ and a real-valued function $f$ defined on the degree set of $G$. The sum of the outputs $f(d_v)$ over all vertices $v\in V(G)$ of $G$ is usually known as the vertex-degree-function indices and is denoted by $H_f(G)$, where $d_v$ represents the degree of a vertex $v$ of $G$. This paper gives sharp bounds on the index $H_f(G)$ in terms of order and size of $G$ when $G$ is connected and has the maximum degree at most $4$. All the graphs achieving the derived bounds are also determined. Bounds involving several existing indices - including the general zeroth-order Randić index and coindex, the general multiplicative first/second Zagreb index, the variable sum lodeg index, and the variable sum exdeg index - are deduced as the special cases of the obtained ones.
