Spectral radius of rooted product of graphs
Presented by Prof. Dragan STEVANOVIC
Type: Oral presentation
Track: Graph Theory
The rooted product of a graph $H$ by a sequence of rooted graphs $G_i$, $i\in V(H)$, is obtained by identifying the vertex $i$ of $H$ with the root of $G_i$. The rooted product of graphs was defined by Godsil and McKay in 1978, and they also determined its characteristic polynomial. Here we consider the special case when all rooted graphs are isomorphic either to a given rooted graph $G$ or to a single-vertex graph (in other words, copies of $G$ are attached to a subset of vertices of $H$ only). We study the behavior of the principal eigenvector of such rooted product and resolve a 2009 conjecture by Belardo, Marzi and Simic on the spectral radius of rooted product of $H$ with a sequence of stars of equal size.