Matchings in Tetrameric 1, 3-Adamantane

Abstract

Suppose $G$ is a graph, $A(G)$ its adjacency matrix, and $\varphi(G,\lambda)=\sum_{i=0}^{n} a_i \lambda^{n-i}$ is the characteristic polynomial of $G$. The polynomial $M(G,x)=\sum_{k \geq 0}(-1)^{k} m(G,k) x^{n-2k}$, is called the matching polynomial of $G$, where $m(G,k)$ is the number of $k-$matchings in $G$. In this paper, we consider tetrameric 1, 3-adamantane, $TA(N)$, and determine some coefficients of characteristic polynomial and matching polynomial of $TA(N)$.