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On the two-sided group digraph with a normal adjacency matrix | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 9، شماره 2، شهریور 2024، صفحه 103-111 اصل مقاله (291.17 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2024.11041.1072 | ||
| نویسندگان | ||
| Farzaneh Nowroozi Larki* 1؛ Shahram Rayat Pisheh2 | ||
| 1Mathematics, Basic Faculty, Shahid Rajaee Teacher Training University | ||
| 2Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University | ||
| تاریخ دریافت: 13 فروردین 1403، تاریخ بازنگری: 27 فروردین 1403، تاریخ پذیرش: 28 اردیبهشت 1403 | ||
| چکیده | ||
| This article explores the adjacency matrix of a two-sided group graph and its properties. We introduce the two-sided color group digraph to generalize the Cayley color graph and the two-sided group digraph. We also obtain the adjacency matrix of the latter digraph and provide a criterion for determining the normality of the adjacency matrix of a two-sided group graph. Moreover, we prove that if all the two-sided group digraphs of valency two for a certain group G are normal, then G is a Hamiltonian group. We also show that if a strongly connected two-sided group digraph of valency two is normal, the corresponding group is isomorphic to the product of two groups: a cyclic group with either Tk,n or Hp,q, or an abelian group. | ||
| کلیدواژه‌ها | ||
| Cayley digraph؛ Adjacency Matrix؛ Normal Matrix | ||
| مراجع | ||
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