Speaker
Wasin So
(San Jose State University)
Description
The energy $\mathcal{E}(G)$ of a graph $G$ is the sum of the absolute values of all the eigenvalues of its adjacency matrix. Gutman (2001) proposed a problem of characterizing the graph $G$ and the edge $e$ of $G$ such that $\mathcal{E}(G-e) \le \mathcal{E}(G)$. Later, Day and So (2008) gave a sufficient condition : $e$ is a cut-edge of $G$.Recently, Tang et al. (2023) gave another sufficient condition for $\mathcal{E}(G-e) \le \mathcal{E}(G)$, where $e$ is not a cut-edge.In this talk, we improve their result by giving a weaker sufficient condition and simplifying their proof. As a consequence, we prove that adding edges to a complete $k$-partite graph leads to higher energy than the energy of the original graph.
Author
Wasin So
(San Jose State University)