Paley-type graphs of order a product of two distinct primes
In this paper, we initiate the study of Paley-type graphs \(\Gamma_N\) modulo \(N=pq\), where \(p,q\) are distinct primes of the form \(4k+1\). It is shown that \(\Gamma_N\) is an edge-regular, symmetric, Eulerian and Hamiltonian graph. Also, the vertex connectivity, edge connectivity, diameter and...
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| Дата: | 2019 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2019
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1443 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | In this paper, we initiate the study of Paley-type graphs \(\Gamma_N\) modulo \(N=pq\), where \(p,q\) are distinct primes of the form \(4k+1\). It is shown that \(\Gamma_N\) is an edge-regular, symmetric, Eulerian and Hamiltonian graph. Also, the vertex connectivity, edge connectivity, diameter and girth of \(\Gamma_N\) are studied and their relationship with the forms of \(p\) and \(q\) are discussed. Moreover, we specify the forms of primes for which \(\Gamma_N\) is triangulated or triangle-free and provide some bounds (exact values in some particular cases) for the order of the automorphism group \(\operatorname{Aut}(\Gamma_N)\) of the graph \(\Gamma_N\), the chromatic number, the independence number, and the domination number of \(\Gamma_N\). |
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