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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Lugansk National Taras Shevchenko University
2019
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admjournalluguniveduua-article-14432019-10-20T08:14:09Z Paley-type graphs of order a product of two distinct primes Das, Angsuman Cayley graph, quadratic residue, Pythagorean prime 05C30, 05C69 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 \(\Gamma_N\). Lugansk National Taras Shevchenko University 2019-10-20 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1443 Algebra and Discrete Mathematics; Vol 28, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1443/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1443/594 Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2019-10-20T08:14:09Z |
| collection |
OJS |
| language |
English |
| topic |
Cayley graph quadratic residue Pythagorean prime 05C30 05C69 |
| spellingShingle |
Cayley graph quadratic residue Pythagorean prime 05C30 05C69 Das, Angsuman Paley-type graphs of order a product of two distinct primes |
| topic_facet |
Cayley graph quadratic residue Pythagorean prime 05C30 05C69 |
| format |
Article |
| author |
Das, Angsuman |
| author_facet |
Das, Angsuman |
| author_sort |
Das, Angsuman |
| title |
Paley-type graphs of order a product of two distinct primes |
| title_short |
Paley-type graphs of order a product of two distinct primes |
| title_full |
Paley-type graphs of order a product of two distinct primes |
| title_fullStr |
Paley-type graphs of order a product of two distinct primes |
| title_full_unstemmed |
Paley-type graphs of order a product of two distinct primes |
| title_sort |
paley-type graphs of order a product of two distinct primes |
| description |
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 \(\Gamma_N\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1443 |
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AT dasangsuman paleytypegraphsoforderaproductoftwodistinctprimes |
| first_indexed |
2025-12-02T15:30:05Z |
| last_indexed |
2025-12-02T15:30:05Z |
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1850412214806118400 |