Cayley Graphs Of Order Research Articles

Pentavalent Cayley graphs of order twice a prime square with solvable automorphism groups

A Cayley graph [Formula: see text] on a finite group [Formula: see text] is said to be normal if the right regular representation [Formula: see text] of [Formula: see text] is normal in the full automorphism group of [Formula: see text]. In this paper, we classify all connected pentavalent non-normal Cayley graphs of order [Formula: see text] with solvable automorphism groups and [Formula: see text] a prime.

New Constructions of Self-Complementary Cayley Graphs

Self-complementary Cayley graphs are useful in the study of Ramsey numbers, but they are relatively very rare and hard to construct. In this paper, we construct several families of new self-complementary Cayley graphs of order $p^4$ where $p$ is a prime and congruent to $1$ modulo $8$.

An Intermediate Value Theorem for the Decycling Numbers of Toeplitz Graphs

In this paper we obtain an intermediate value theorem for the decycling numbers of Toeplitz graphs: if $$n \ge 3$$n?3, and $$0 \le r \le n - 2$$0≤r≤n-2, then there exists a Toeplitz graph of order $$n$$n with decycling number $$r$$r. We also prove that the decycling numbers of connected Cayley graphs of order $$n$$n satisfy the intermediate value property if and only if $$n = 4$$n=4 or $$6$$6.

Cayley graphs of order [formula omitted] are Hamiltonian

Suppose G is a finite group, such that |G|=30p, 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).