In this paper, the structure of directed strongly regular $2$-Cayley graphs of cyclic groups is investigated. In particular, the arithmetic conditions on parameters $v, k,\mu,\lambda$, and $t$ are given. Also, several infinite families of directed strongly regular graphs which are also 2-Cayley digraphs of abelian groups are constructed.
COBISS.SI-ID: 1024426836
This discussion is published in the esteemed general scientific mathematical journal Proc. Lond. Math. Soc. that ranks in A' (ARRS methodology). It solves the hamiltonicity problem for cubic Cayley graphs on groups with respect to genereting sets consisting of an involution, a non-involution of odd order and the inverse of this non-involution.
COBISS.SI-ID: 1024390740
In this paper it is poved 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 Hamilton cycle. More precisely, if p, q, and r are distinct primes, then n can be of the form kp with 24 \ne k ( 32, or of the form kpq with k ≤ 5, or of the form pqr, or of the form kp^2 with k ≤ 4, or of the form kp^3 with k ≤ 2.
COBISS.SI-ID: 1024371028
In this paper it is shown that every connected vertex-transitive graph of order 10p, p a prime different from 7, which is not isomorphic to a quasiprimitive graph arising from the action of PSL(2,k) on cosets of Z_k\rtimes Z_{(k-1)/10}, contains a Hamilton path.
COBISS.SI-ID: 1024409428
A graph X is said to be an m-Cayley graph on a non-trivial group G if its automorphism group contains a semiregular subgroup isomorphic to G having m orbits on the vertex set of X. If G is cyclic and m = 1, 2, 3, 4, or 5 then X is said to be a circulant, a bicirculant, a tricirculant, a tetracirculant, or a pentacirculant, respectively. A graph is said to be symmetric if its automorphism group acts transitively on the set of its arcs. All cubic symmetric circulants, bicirculants and tricirculants are known, and in this paper we give complete classifications of cubic symmetric tetracirculants and pentacirculants. In particular, it is shown that there are infinitely many connected cubic symmetric tetracirculants whereas there are only two connected cubic symmetric pentacirculants.
COBISS.SI-ID: 1024446036