A graph is semi-symmetric if it is regular and edge transitive but not vertex transitive. The 3and 4-valent semi-symmetric graphs are wellstudied. Several papers describe infinite families of such graphs and their properties. 3-valent semi-symmetric graphs have been completely classified up to 768 vertices. The goal of this project is to extend this work to 5-valent semi-symmetric graphs. In th...

In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if {Gk}k>1 is a set of connected graphs such that Gk has k vertices for each k, then the set of all chromatic symmetric functions {XGk}k>1 generates the algebra of symmetric functions. We also obtain explicit expressions for the generators arising ...

The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.

Symmetric and semisymmetric graphs are used in many scientific domains, especially parallel computation and interconnection networks. The industry and the research world make a huge usage of such graphs. Constructing symmetric and semisymmetric graphs is a large and hard problem. In this paper a tool called G-graphs and based on group theory is used. We show the efficiency of this tool for cons...

This paper determines all arc-transitive pentavalent graphs of order 4pq, where q > p > 5 are primes. The cases p = 1, 2, 3 and p = q is a prime have been treated previously by Hua et al. [Pentavalent symmetric graphs of order 2pq, Discrete Math. 311 (2011), 2259-2267], Hua and Feng [Pentavalent symmetric graphs of order 8p, J. Beijing Jiaotong University 35 (2011), 132-135], Guo et al. [Pentav...