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## March 2019

### Refinements of metrics (Wai Yan Pong, CSUDH)

I will talk about a few graph-theoretic metrics then introduce the concept of refinements on a class of functions that include all metrics. As a case study, we will construct various refinements on the shortest-path distance. Consequently, we obtain a few "better" versions of the Erdos number. In the course of our investigation, we realized various construction of metrics can be unified under a rather natural concept that we called monotonic monoid norm. This is a joint work with Kayla Lock and Alex…

Find out more »## April 2019

### Theory of vertex Ho-Lee-Schur graphs (Sin-Min Lee, SJSU)

A triple of natural numbers (a,b,c) is an S-set if a+b=c. I. Schur used the S-sets to show that for n >3, there exists s(n) such that for prime p > s(n), x^p + y^p = z^p (mod p) has a nontrivial solution. A (p,q)-graph G is said to be vertex Ho-Lee-Schur graph if there exists a bijection f: V(G) --> {1,2,…,p} such that for each C3 subgraph of G with vertices {x,y,z} the triple (f(x),f(y),f(z)) is an S-set. The VHLS deficiency of…

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