On weakly symmetric graphs of order twice a prime

Pentavalent symmetric graphs of order twice a prime power

Classifying pentavalnet symmetric graphs of order $24p$

A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2, 3, 5, 11 or 17, and up to isomorphism, there are only eleven such graphs.

Symmetric graphs of order 4p of valency prime

A graph is symmetric or arc-transitive if its automorphism group acts transitively on vertices, edges and arcs. Let p, q be odd primes with p, q ≥ 5 and X a q-valent symmetric graph of order 4p. In this paper, we proved that X K4p with 4p-1=q, X K2p,2p-2pK2 with 2p-1=q, the quotient graph of X is isomorphic to Kp,p and p=q, or K2p and 2p-1=q.

Cubic symmetric graphs of order a small number times a prime or a prime square

A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular elementary abelian coverings of the complete bipartite graph K3,3 and the s-regular cyclic or elementary abelian coverings of the complete graph K4 for each s 1 are classified when the fibrepreserving automorphism groups act arc-transitively. A new infinite family of cubic 1-regu...

A note on 3-Prime cordial graphs

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....