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...

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify tetravalent symmetric graphs of order 9p for each prime p.

Detecting protein complexes is an important way to discover the relationship between network topological structure and its functional features in protein-protein interaction (PPI) network. The spectral clustering method is a popular approach. However, how to select its optimal Laplacian matrix is still an open problem. Here, we analyzed the performances of three graph Laplacian matrices (unnorm...

We compute an explicit e-positive formula for the chromatic symmetric function of a 3 lollipop graph, Lm,n. From here we deduce that there exist countably infinite distinct e-positive, and 4 hence Schur-positive, bases of the algebra of symmetric functions whose generators are chromatic 5 symmetric functions. Finally, we resolve 6 conjectures on the chromatic symmetric function of a 6 lariat gr...

A digraph is a symmetric cycle if it is symmetric and its underlying graph is a cycle. It is proved that if D is an asymmetric digraph not containing a symmetric cycle, then D remains asymmetric after removing some vertex. It is also showed that each digraph D without a symmetric cycle, whose underlying graph is connected, contains a vertex which is a common fixed point of all automorphisms of D.