The Department of Mathematics at Western Michigan University will present a graph theory seminar on Fridays.
The number of paths and cycles in a digraph presented by Laars Helenius, Western Michigan University
Abstract: Let D be a digraph and let L be any k + 1 sequence of vertices from D. Then L is a simple k-sequence when it represents a path or cycle of length k in D. An algorithm is presented for constructing from the adjacency matrix A of a digraph the matrix of its simple k-sequences Ak. In this matrix aij(k) gives the number of paths starting at vi and ending at vj when i ≠ j and the number of cycles containing vi when i = j.
From graph automorphism to network alignment presented by Duy Duong-Tran, Purdue University
Abstract: Graph automorphism has a long history dated back to Frutch's Theorem (1939) which states that for every fi