论文标题
具有固定数量吊坠或切割顶点的图形的总偏心指数
Total eccentricity index of graphs with fixed number of pendant or cut vertices
论文作者
论文摘要
连接图的总偏心率指数定义为其所有顶点的偏心率的总和。我们用$ \ Mathfrak {h} _ {n，k} $表示$ n $顶点上的所有连接图表，并用$ n $ n $ VERTICES上的所有连接图表示，$ s $ s $ cut cut Tertices by $ \ mathfrak {在本文中，我们在$ \ mathfrak {h} _ {n，k} $上的总偏心索引上给出了尖锐的下限和上限，而在$ \ mathfrak {c_ {n，s}} $上的相同的敏锐下限。当$ s = 0,1，n-3，n-2 $时，我们还提供了超过$ \ mathfrak {c_ {n，s}} $的总偏心指数的尖锐上限
The total eccentricity index of a connected graph is defined as sum of the eccentricities of all its vertices. We denote the set of all connected graphs on $n$ vertices with $k$ pendant vertices by $\mathfrak{H}_{n,k}$ and denote the set of all connected graphs on $n$ vertices with $s$ cut vertices by $\mathfrak{C_{n,s}}$. In this paper, we give the sharp lower and upper bounds on the total eccentricity index over $\mathfrak{H}_{n,k}$ and the sharp lower bound for the same over $\mathfrak{C_{n,s}}$. We also provide the sharp upper bounds on the total eccentricity index over $\mathfrak{C_{n,s}}$ when $s=0,1,n-3,n-2$ and propose a problem regarding the upper bound over $\mathfrak{C_{n,s}}$ for $2\leq s\leq n-4.$
