عدد اول فرد p، 2p^5گراف های نیم متقارن از مرتبه

Subject Areas : Algebra

پوریا مجدآملی ¹ , محمدرضا درفشه ²

1 - دانشگاه ازاد
2 - Department of Computer, Faculty of Mathematics-Statistics and Science, University of Tehran

Received: 2022-02-05 Accepted : 2022-09-18 Published : 2024-01-18

Keywords: گراف رأس انتقالی, رده بندی گراف‌های مکعبی نیم متقارن, گراف نیم متقارن, گراف یال انتقالی,

Abstract :

A simple graph is called semi-symmetric if it is regular and edge transitive but not vertex transitive. In this paper we prove that there is no connected cubic semi-symmetric graph of order 2p^5 in special case and where p is a prime number and p> 3 and p≠7. In this paper all graphs are finite and undirected and simple. The class of semi-symmetric graphs was first studied by Folkman who found several infinite families of such graphs and posed eight open problems. Folkman proved that there are no semi-symmetric graphs of order 2p or 2p^2 for any prime p.Then the authors prove that there is no connected cubic semi-symmetric graph of order 2p^3 for any prime p>3 and that for p=3 the Gray graph is the only connected cubic semi-symmetric graph of order 2p^3. Also it is proved that a connected cubic semi-symmetric graph of order 2p^3. Also it is proved that a connected cubic semi-symmetric graph of order 6p^3 exists if and only if p-1 is divisible by 3.

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