论文标题
有限基团的非交通图的频谱和能量
Spectrum and energy of non-commuting graphs of finite groups
论文作者
论文摘要
令$ g $为有限的非阿布尔组，$γ_{nc}（g）$是其非公认图。在本文中，我们计算某些有限组的$γ_{nc}（g）$的光谱和能量。由于我们的结果，我们构建了整体$ r $ - 分段图的无限家族。我们比较能量和laplacian的能量（由$ e（γ_{nc}（g））$和$ le（分别为γ_{nc}（g））$的$γ_{nc {nc}（g）$表示，并得出$ e（γ_{nc}（g））$ e（nc}（g）$ que（for）$ que（g）for（g）for（g）（g）非亚伯式的订单$ PQ $。这表明[Gutman，I.，Abreu，N。M. M.，Vinagre，C.T.M.，Bonifacioa，A。S和Radenkovic，S。数学。计算。 Chem。，59：343--354，（2008）]不适合某些有限群体的非公告图，这也为上述猜想产生了反式例子的新家族。
Let $G$ be a finite non-abelian group and $Γ_{nc}(G)$ be its non-commuting graph. In this paper, we compute spectrum and energy of $Γ_{nc}(G)$ for certain classes of finite groups. As a consequence of our results we construct infinite families of integral complete $r$-partite graphs. We compare energy and Laplacian energy (denoted by $E(Γ_{nc}(G))$ and $LE(Γ_{nc}(G))$ respectively) of $Γ_{nc}(G)$ and conclude that $E(Γ_{nc}(G)) \leq LE(Γ_{nc}(G))$ for those groups except for some non-abelian groups of order $pq$. This shows that the conjecture posed in [Gutman, I., Abreu, N. M. M., Vinagre, C. T.M., Bonifacioa, A. S and Radenkovic, S. Relation between energy and Laplacian energy, MATCH Commun. Math. Comput. Chem., 59: 343--354, (2008)] does not hold for non-commuting graphs of certain finite groups, which also produces new families of counter examples to the above mentioned conjecture.
