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Spectrum of proper power graphs of the direct product of certain finite groups
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2021-05-06 , DOI: 10.1080/03081087.2021.1918051
Sayyed Heidar Jafari 1 , Sriparna Chattopadhyay 2
Affiliation  

The proper power graph P(G) of a group G is the simple graph with non-trivial elements of G as vertices and two distinct elements are adjacent if and only if one is a power of the other. The aim of this paper is to find the structure and to compute the spectrum of the proper power graph of direct product of two finite groups G1 and G2, where at least one of G1 and G2 is an EPO group. Also we provide the full spectrum and hence the energy of P(G1×G2) whenever both G1 and G2 are EPO groups.



中文翻译:

某些有限群的直积的固有幂图的谱

正确的功率图P(G)G的一个简单图是以G的非平凡元素为顶点,并且两个不同的元素相邻当且仅当一个元素是另一个元素的幂时。本文的目的是寻找结构并计算两个有限群直积的本征幂图的谱G1个G2个,其中至少一个G1个G2个是一个 EPO 组。我们还提供全光谱,因此提供能量P(G1个×G2个)每当两者G1个G2个是 EPO 组。

更新日期:2021-05-06
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