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 16p is given for each prime p. It fo...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 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.展开更多
基金Supported by the National Natural Science Foundation of China(No.11301154,11301151,11201401,11271012)the Key Project of Education Department of Henan Province Scientific and Technological Research(No.13A110249)the Scientific Research Foundation for Doctoral Scholars of HAUST(No.09001707)
文摘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 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.
