论文标题
Equienergentic非同一统一的Cayley图形图
Integral equienergetic non-isospectral unitary Cayley graphs
论文作者
论文摘要
我们证明Cayley图$ x（g，s）$和$ x^+（g，s）$对于任何Abelian Group $ g $和任何对称的子集$ S $来说都是均等的。然后，我们专注于统一Cayley图的家族$ g_r = x（r，r^*）$，其中$ r $是具有身份的有限交换戒指。我们表明，在温和的条件下，$ \ {g_r，g_r^+\} $是一对积分的equienergetic非镜头图（通常连接和非双分部分）。然后，我们获得的条件使得$ \ {g_r，\ bar g_r \} $是equienergetic非镜头图。最后，我们表征了所有积分equienergetic非镜头三元$ \ {g_r，g_r^+，\ bar g_r \} $，使所有图形也是Ramanujan。
We prove that the Cayley graphs $X(G,S)$ and $X^+(G,S)$ are equienergetic for any abelian group $G$ and any symmetric subset $S$. We then focus on the family of unitary Cayley graphs $G_R=X(R,R^*)$, where $R$ is a finite commutative ring with identity. We show that under mild conditions, $\{G_R, G_R^+\}$ are pairs of integral equienergetic non-isospectral graphs (generically connected and non-bipartite). Then, we obtain conditions such that $\{G_R, \bar G_R\}$ are equienergetic non-isospectral graphs. Finally, we characterize all integral equienergetic non-isospectral triples $\{G_R, G_R^+, \bar G_R \}$ such that all the graphs are also Ramanujan.
