1.

Partial sum quadruples and bi-Abelian digraphs

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

2.

Hamilton cycles in (2, odd, 3)-Cayley graphs

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

3.

Hamiltonian cycles in Cayley graphs whose order has few prime factors

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