Aniruddha Samanta

Energy of signed graphs and the vertex cover number

The energy $\mathcal{E}(\Gamma)$ of a signed graph $\Gamma=(G,\sigma)$ is the sum of the absolute values of the eigenvalues of its adjacency matrix $A(\Gamma)$. In this article, we prove that $\mathcal{E}(\Gamma)\geq 2\tau(G)$, where $\tau(G)$ is the vertex cover number of $G$. The case of unsigned graphs, a 1980s conj...