## Number Theory Seminar

### Tuesday, November 20th, 2018

**Time:** 10:00-11:00 a.m. **Place:** Jeffery Hall 422

**Speaker:** Siqi Li (Queen's University)

**Title:** Realizability of a set of integers as degrees of the vertices of a linear graph.

**Abstract:** In this talk, we consider the following problem: Let A be a non-decreasing sequence of positive integers of length n. Does there exist a graph G on n vertices v_1 to v_n such that A is the sequence formed by deg(v_1) to deg(v_n)? Furthermore, the realizability of a connected graph, simple graph and the biconnected graph for a given finite sequence of vertices degrees A is considered. The application of the above theorem involves the description of the structure for isomers in an organic chemical compound.