Pentavalent symmetric graphs of order 16p

Abstract

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 12p is given for each prime p. As a result, a connected pentavalent symmetric graph of order 12p exists if and only if p = 2, 3, 5 or 11, and up to isomorphism, there are only nine such graphs: one for each p = 2, 3 and 5, and six for p = 11.

Pentavalent arc-transitive Cayley graphs on Frobenius groups with soluble vertex stabilizer

“…Since there exists no connected arc-transitive pentavalent graphs of order p for each prime p ≥ by [18, Theorem 1.1], the former case does not occur. By [17], there exists no connected arc-transitive pentavalent graphs of order , so the latter case is excluded. Similarly, we also exclude the case where Γ F ∼ = K .…”

Heptavalent Symmetric Graphs of Order 16p

“…Guo [10] determined the exact structure of pentavalent case. Following this structure, a series of pentavalent symmetric graphs was classified in [15,19,20,26,27,12]. Recently, Guo [11] gave the exact structure of heptavalent case.…”

On basic graphs of symmetric graphs of valency five

“…In the literature, there are lots of works in classifying symmetric graphs of order kp n and small valency d, especially with n and k small and d = 3, 4, or 5; see [6,7,12,13,24,25,27] for example. In particular, cubic or pentavalent symmetric basic graphs of order 2p n for variable prime p and integer n were classified completely in [6,7], and tetravalent 2-arc-transitive basic graphs of order 2p n were classified in [27].…”