论文标题
通勤共轭类的属群体图
Genus of commuting conjugacy class graph of groups
论文作者
论文摘要
对于非阿布莱亚集团$ g $，其通勤共轭类图$ \ Mathcal {ccc}（g）$是一个简单的无向图，其顶点集是$ g $的非中心元素的一组共轭类别，如果有两个不同的$ x^g $ and $ y^g $ y $ x^$ x^$ x^$ x^y' y^g $，以至于$ x'y'= y'x'$。在本文中，我们计算了六个众所周知的非亚伯利亚两生成组的$ \ MATHCAL {CCC}（g）$（viz。$ d_ {2n}，sd_ {8n}，q_ {8n}，q_ {4m}这些组的$ \ MATHCAL {CCC}（G）$是平面，环形，双螺白或三螺旋体。
For a non-abelian group $G$, its commuting conjugacy class graph $\mathcal{CCC}(G)$ is a simple undirected graph whose vertex set is the set of conjugacy classes of the non-central elements of $G$ and two distinct vertices $x^G$ and $y^G$ are adjacent if there exists some elements $x' \in x^G$ and $y' \in y^G$ such that $x'y' = y'x'$. In this paper we compute the genus of $\mathcal{CCC}(G)$ for six well-known classes of non-abelian two-generated groups (viz. $D_{2n}, SD_{8n}, Q_{4m}, V_{8n}, U_{(n, m)}$ and $G(p, m, n)$) and determine whether $\mathcal{CCC}(G)$ for these groups are planar, toroidal, double-toroidal or triple-toroidal.
