A classification of cubic symmetric graphs of order 16p 2

Abstract

A graph is called symmetric if its automorphism group acts transitively on its arc set. In this paper, we classify all connected cubic symmetric graphs of order 16 p 2 for each prime p.

Classifying cubic symmetric graphs of order $18 p^2$

“…Since p ≥ 7 and A is a {2, 3, p}-group, by [18, pp. 12-14] and [9], T is one of the following groups: PSL(2, 7), PSL (2,8), PSL (2,17), and PSL (3,3)…”

“…Let T be a spanning tree of F 18 , as shown by dart lines in Figure 1. p is defined by φ = 0 on T and φ = (1, 0), (0, 1), (0, −1), (0, 1), (0, −1), (1, 1), (0, 0), (1, 0), (0, 0), and (1, 0) on the cotree arcs (1, 2), (2, 3), (3,4), (4, 5), (5,6), (1, 7), (7,14), (13,8), (14,9), and (11,18), respectively. By [23, Theorem 3.1], we have the following lemma.…”

“…Feng and Kwak [15] classified cubic symmetric graphs of order a small number times a prime or a prime square. Following this, classifications of cubic s-regular graphs of orders 4p i , 6p i , 8p i , 10p i , 16p i , 12p i , 22p i , 36p i for i = 1, 2 and prime integer p were presented in [12,16,3,25,1,27,4]. Furthermore, cubic s-regular graphs of orders 2p 3 , 14p, 6p 3 , 28p, and 4m where m is an odd integer were classified in [17,24,2,20,7].…”