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Algebra and Discrete Mathematics, 2019, том 28, выпуск 1, страницы 44–59
(Mi adm713)
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RESEARCH ARTICLE
Paley-type graphs of order a product of two distinct primes
Angsuman Das Department of Mathematics, Presidency University, Kolkata 86/1, College Street, Kolkata 700073, India
Аннотация:
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 $\Gamma_N$.
Ключевые слова:
Cayley graph, quadratic residue, Pythagorean prime.
Поступила в редакцию: 02.02.2015 Исправленный вариант: 27.08.2019
Образец цитирования:
Angsuman Das, “Paley-type graphs of order a product of two distinct primes”, Algebra Discrete Math., 28:1 (2019), 44–59
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm713 https://www.mathnet.ru/rus/adm/v28/i1/p44
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