论文标题
有限组的通勤共轭类别图的光谱方面
Spectral aspects of commuting conjugacy class graph of finite groups
论文作者
论文摘要
The commuting conjugacy class graph of a non-abelian group $G$, denoted by $\mathcal{CCC}(G)$, 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' \在y^g $中，以至于$ x'y'= y'x'$。在本文中，我们计算了$ d_ {2n}，q_ {4m}，u _ {（n，m）}，v_ {8n} $和$ sd_ {8n} $的各组的各种光谱和能量。我们的计算表明，对于这些组而言，$ \ MATHCAL {CCC}（G）$是超级不可或缺的。我们比较了各种能量，因此观察到$ \ Mathcal {ccc}（g）$满足Gutman等人的E-LE猜想。我们还为Dutta等人提出的问题提供了负面答案。比较拉普拉斯和无价的拉普拉斯能量。最后，我们通过表征上述组$ g $来结束本文，以使$ \ mathcal {ccc}（g）$具有超能量，l-hyperenergetic或q-hyperenergetic。
The commuting conjugacy class graph of a non-abelian group $G$, denoted by $\mathcal{CCC}(G)$, 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 various spectra and energies of commuting conjugacy class graph of the groups $D_{2n}, Q_{4m}, U_{(n, m)}, V_{8n}$ and $SD_{8n}$. Our computation shows that $\mathcal{CCC}(G)$ is super integral for these groups. We compare various energies and as a consequence it is observed that $\mathcal{CCC}(G)$ satisfy E-LE Conjecture of Gutman et al. We also provide negative answer to a question posed by Dutta et al. comparing Laplacian and Signless Laplacian energy. Finally, we conclude this paper by characterizing the above mentioned groups $G$ such that $\mathcal{CCC}(G)$ is hyperenergetic, L-hyperenergetic or Q-hyperenergetic.
