Algebraic Graph Theory Seminar - Róbert Jajcay (11.11.2022)

Friday 11.11.2022 at 13:00, Lecture room M/V (online too)

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prof. RNDr. Róbert Jajcay, DrSc.:
Bounds for the energy of graphs

(AGT in Bratislava team, scheduled meeting)

Abstract:
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.

 

 

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