Hołubowski, WaldemarKozerenko, SergiyOliynyk, BogdanaSolomko, Viktoriia2025-01-292025-01-292024The Unitary Cayley Graph of Upper Triangular Matrix Rings / Waldemar Hołubowski, Sergiy Kozerenko, Bogdana Oliynyk, Viktoriia Solomko - [S. l.] : arXiv, 2024. - 9 p. - https://doi.org/10.48550/arXiv.2403.01303https://ekmair.ukma.edu.ua/handle/123456789/33367The unitary Cayley graph CR of a finite unital ring R is the simple graph with vertex set R in which two elements x and y are connected by an edge if and only if x − y is a unit of R. We characterize the unitary Cayley graph CTn(F) of the ring of all upper triangular matrices Tn(F) over a finite field F. We show that CTn(F) is isomorphic to the semistrong product of the complete graph Km and the antipodal graph of the Hamming graph A(H(n, pk)), where m = p kn(n−1) 2 and |F| = pk. In particular, if |F| = 2, then the graph CTn(F) has 2n−1 connected components, each component is isomorphic to the complete bipartite graph Km,m, where m = 2 n(n−1) 2 . We also compute the diameter, triameter, and clique number of the graph CTn(F).enunitary Cayley graphupper triangular matrix ringantipodal graphHamming graphclique numberpreprintPreprinthttps://doi.org/10.48550/arXiv.2403.01303