Seminár z algebraickej teórie grafov - Róbert Jajcay (11.11.2022)

v piatok 11.11.2022 o 13:00 hod. v miestnosti M/V aj online formou

09. 11. 2022 10.31 hod.
Od: Martin Mačaj

Prednášajúci: prof. RNDr. Róbert Jajcay, DrSc.,

Názov: Bounds for the energy of graphs

Termín: 11.11.2022, 13:00 hod., M V a MS Teams (AGT in Bratislava teamscheduled meeting)

Let $G$ be a graph with $n$ vertices, and let $\lambda_{1}\geq\ldots\geq \lambda_{n}$ be the eigenvalues of (the adjacency matrix $A$ of) $G$. The energy $E(G)$ of $G$ is defined to be the sum of the absolute values of the eigenvalues of $G$, $E(G)=|\lambda_{1}|+\ldots+|\lambda_{n}|$. Several upper and lower bounds for this parameter can be found in literature; for example, the energy of a graph $G$ is known to be greater than or equal to twice the minimum degree of $G$. In this talk, we present further results and improvements for these bounds based on joint papers of the presenter, Slobodan Filipovski and Ivan Gutman.

Those of you who are not able to attend in person or who are still uncertain about the safety of attending in person are welcome to attend via MS Teams. In either case, we hope to see as many of you as possible (either in person or virtually) at our Friday gatherings.