We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity and as well as the full spectrum distribution. For an integer d in , we

Extremal questions for vertex colorings of graphs For graphs $G$ and $H$, an $H$-coloring of $G$ is a map from the vertices of $G$ to the vertices of $H$ so that an edge in $G$ is mapped to an edge

Graph polynomials In this talk, I will discuss various aspects of several graph polynomials such as the location of their roots, their combinatorial properties and extremal questions. Join Zoom Meeting: link

An Unsupervised Framework for Comparing Graph Embeddings The goal of many machine learning applications is to make predictions or discover new patterns using graph-structured data as feature information. In order to extract useful structural information from graphs, one might want

Conditions for perfect matchings in random sparse bipartite graphs Given a uniformly random sparse matrix A, with specified number of nonzero entries in columns and rows, we determine when A has full row rank over a finite field. As a

Colourings, Polynomials and Roots A lot has happened since graph colourings first arose as an applied problem in cartography – do four colours always suffice to distinguish countries when colouring a map? Along the way to the proof, the related

Progress towards the Burning Number Conjecture The burning number b(G) of a graph G is the smallest integer k such that G can be covered by k balls of radii respectively 0,...,k-1, and was introduced independently by Brandenburg and Scott at Intel as a transmission problem on processors and Bonato, Janssen

Speaker 1: Isaac McMullin Existence of Optimal Split Reliability Polynomials One of the most common models of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability p. On one hand, one

Avoiding additive powers in words A word is a sequence of symbols taken from some finite alphabet. A square is a word of the form xx, where x is a nonempty word. It is well-known that there are infinite words