Geodesic
Paley-type graphs of order a product of two distinct primes
Algebra and discrete mathematics, Tome 28 (2019) no. 1, pp. 44-59

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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 $\Gamma_N$.
Keywords: Cayley graph, quadratic residue, Pythagorean prime. 
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     author = {Angsuman Das},
     title = {Paley-type graphs of order a product of two distinct primes},
     journal = {Algebra and discrete mathematics},
     pages = {44--59},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_28_1_a3/}
}
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Angsuman Das. Paley-type graphs of order a product of two distinct primes. Algebra and discrete mathematics, Tome 28 (2019) no. 1, pp. 44-59. http://geodesic.mathdoc.fr/item/ADM_2019_28_1_a3/