https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 On automorphism groups of graph truncations https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28295 t on t vertices. We determine necessary and sufficient conditions for T(Γ) to be hamiltonian, show Aut(T(Γ)) ≅ Aut(Γ), as well as show that if Γ  is vertex-transitive, then T(Γ ) is vertex-transitive if and only if Γ  is arc-transitive. Finally, in the case where t is prime we determine necessary and sufficient conditions for T(Γ) to be isomorphic to a Cayley graph as well as an additional necessary and sufficient condition for T(Γ) to be vertex-transitive.]]> Wed 11 Apr 2018 16:03:05 AEST ]]> Hamilton paths in Cayley graphs on Coxeter groups: I https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28294 n, Bn, and Dn with regard to the problem of whether they are Hamilton-laceable or Hamilton-connected. It is known that every connected bipartite Cayley graph on An, n ≥ 2, whose connection set contains only transpositions and has valency at least three is Hamilton-laceable. We obtain analogous results for connected bipartite Cayley graphs on Bn, and for connected Cayley graphs on Dn. Non-bipartite examples arise for the latter family.]]> Thu 17 Sep 2020 09:45:52 AEST ]]> Reliability of interconnection networks https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:35348 Thu 01 Aug 2019 15:36:55 AEST ]]> Hamilton paths in Cayley graphs on generalized dihedral groups https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11211 Sat 24 Mar 2018 08:12:45 AEDT ]]> Vertex-transitive graphs of prime-squared order are Hamilton-decomposable https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:17871 Sat 24 Mar 2018 07:56:12 AEDT ]]> Pancyclicity and Cayley graphs on abelian groups https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:16258 Sat 24 Mar 2018 07:54:17 AEDT ]]> Pancyclicity and Cayley graphs on generalized dihedral groups https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:30205 Sat 24 Mar 2018 07:31:04 AEDT ]]> The 2-good-neighbor diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM* model https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:24872 n generated by the transposition tree Γn has many good properties. In this paper, we give that the 2-good-neighbor diagnosability of CΓn under the PMC model and MM⁎ model is g(n−2)−1, where n≥4and g is the girth of CΓn.]]> Sat 24 Mar 2018 07:11:20 AEDT ]]> The 1-good-neighbour diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM* model https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:32988 et al. proposed a new measure for fault tolerance of the system, which is called g-good-neighbour diagnosability that restrains every fault-free node containing at least g fault-free neighbours. As a favourable topology structure of interconnection networks, the Cayley graph CΓn generated by the transposition tree Γn has many good properties. In this paper, we give that the 1-good-neighbour diagnosability of CΓn under the PMC model and MM∗ model is 2n−3 except the bubble-sort graph B₄ under MM∗ model, where n≥4, and the 1-good-neighbour diagnosability of B₄ under the MM∗ model is 4.]]> Fri 17 Aug 2018 15:44:20 AEST ]]>