Morris, Joyhttps://hdl.handle.net/10133/49412019-10-21T12:28:39Z2019-10-21T12:28:39ZStrongly regular edge-transitive graphsMorris, JoyPraeger, Cheryl E.Spiga, Pablohttps://hdl.handle.net/10133/51652018-07-10T19:53:08Z2009-01-01T00:00:00ZStrongly regular edge-transitive graphs
Morris, Joy; Praeger, Cheryl E.; Spiga, Pablo
In this paper, we examine the structure of vertex- and edge-transitive strongly regular graphs,using normal quotient reduction. We show that their reducible graphs in this family have quasi primitive automorphism groups, and prove (using the Classiﬁcation of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also ﬁnd some constraints on the parameters of the graphs in this family that reduce to complete graphs
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2009-01-01T00:00:00ZHamiltonian cycles in Caley graphs whose order has few prime factorsKutnar, KlavdijaMarusic, DraganMorris, Dave WitteMorris, JoySparl, Primozhttps://hdl.handle.net/10133/51642018-07-10T19:31:32Z2012-01-01T00:00:00ZHamiltonian cycles in Caley graphs whose order has few prime factors
Kutnar, Klavdija; Marusic, Dragan; Morris, Dave Witte; Morris, Joy; Sparl, Primoz
We prove that if Cay(G;S) is a connected Cayley graph with n vertices,and the prime factorization of n is very small, then Cay(G;S) has a hamiltonian cycle. More precisely, if p, q, and r are distinct primes, then n can be of the form kp with 24 6= k < 32, or of the form kpq with k ≤ 5,or of the form pqr,or of the form kp2 with k ≤ 4,or of the form kp3 with k ≤ 2.
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2012-01-01T00:00:00ZCaley graphs of order 16p are hamiltonianCurran, Stephen J.Morris, Dave WitteMorris, Joyhttps://hdl.handle.net/10133/51632018-07-10T18:27:14Z2012-01-01T00:00:00ZCaley graphs of order 16p are hamiltonian
Curran, Stephen J.; Morris, Dave Witte; Morris, Joy
Suppose G is a ﬁnite group, such that |G| = 16p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S).
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2012-01-01T00:00:00ZOn the automorphism groups of almost all circulant graphs and digraphsBhoumik, SoumyaDobson, EdwardMorris, Joyhttps://hdl.handle.net/10133/51622018-07-10T18:01:23Z2018-01-01T00:00:00ZOn the automorphism groups of almost all circulant graphs and digraphs
Bhoumik, Soumya; Dobson, Edward; Morris, Joy
We attempt to determine the structure of the automorphism group of a generic circulant graph. We ﬁrst show that almost all circulant graphs have automorphism groups as small as possible. The second author has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism group is not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose order is in a “large” subset of integers. We note that all non-normal circulant (di)graphs can be classiﬁed into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph.
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2018-01-01T00:00:00Z