论文标题
零除数图的偏心拓扑索引$γ[\ mathbb {z} _n] $
Eccentric Topological Index of the Zero Divisor graph $Γ[\mathbb {Z}_n]$
论文作者
论文摘要
$γ[r] $表示的交换环$ r $的零除数图是一个图形，其顶点为$ r $的非零零除数，如果它们的产品为零，则两个顶点相邻。化学图理论是数学化学的一个分支，它涉及图论在解决分子问题方面的非平凡应用。包含有限交换环的图在机器人技术，信息和通信理论，椭圆曲线和密码学，物理和统计数据中也具有广泛的应用。在本文中，我们考虑零除数图$γ[\ mathbb {z} _ {p^n}] $，其中$ p $是素数。我们得出了偏心连接索引的标准形式，增强的偏心连接指数和零除数图$γ[\ mathbb {z} _ {p^n}] $的EDIZ偏心连接指数。
The Zero divisor Graph of a commutative ring $R$, denoted by $Γ[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptical curve and cryptography, physics and statistics. In this paper, we consider the zero divisor graph $Γ[\mathbb{Z}_{p^n}]$ where $p$ is a prime. We derive the standard form of the Eccentric Connectivity Index, Augmented Eccentric Connectivity Index, and Ediz Eccentric Connectivity Index of the zero divisor graph $Γ[\mathbb{Z}_{p^n}]$.
