线性亚苯基Schultz不变量的基多项式
Base Polynomials for Schultz Invariants of Linear Phenylenes
摘要：
令$L_{n}$为线性$[n]$亚苯基的分子图，$L'_{n}$为通过将四元环连接到$L_{n-1}$的末端六边形而获得的图。因此，$L'_{n}$是$[n-1]$亚苯基的$α,ω$ -二环丁二烯衍生物的分子图，包含$n-1$六边形和$n$正方形.在本文中，我们给多项式作为基础的舒尔茨不变量。实际上，我们用多项式表示$L_{n}$和$L'_{n}$的2-2、2-3和3-3次顶点之间的路径长度，这些多项式用于找到舒尔茨多项式、修正舒尔茨多项式、舒尔茨指数和修正舒尔茨指数。
英文摘要：
Let $L_{n}$ be the molecular graph of linear $[n]$phenylene, and $L'_{n}$ the graph obtained by attaching 4-membered cycles to terminal hexagons of $L_{n-1}$. Thus, $L'_{n}$ is the molecular graph of the $α,ω$ - dicyclobutadieno derivative of $[n-1]$phenylene, containing $n-1$ hexagons and $n$ squares. In this paper we give polynomials which serve as bases for Schultz invariants. Actually, we represent lengths of paths among vertices of degrees 2-2, 2-3, and 3-3 of $L_{n}$ and $L'_{n}$ in terms of polynomials, which are used to find Schultz polynomial, modified Schultz polynomial, Schultz index, and modified Schultz index.
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