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عدد اول فرد p، 2p^5گراف های نیم متقارن از مرتبه | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 شهریور 1401 | ||
| نوع مقاله: research paper | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2022.65488.2209 | ||
| نویسندگان | ||
پوریا مجدآملی 1؛ محمدرضا درفشه  2
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| 1دانشجوی دکتری/دانشگاه آزاد | ||
| 2عضو هیات علمی گروه ریاضی دانشگاه تهران | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| semi-symmetric graph؛ vertex transitive graph؛ edge transitive graph؛ classification of cubic semi-symmetric graphs | ||
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آمار تعداد مشاهده مقاله: 57 |
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