1.

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

2.

Hamilton paths in vertex-transitive graphs of order 10p

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

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 ≠ 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