Author

K. Das

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Preprint Oct 2026

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...

Aniruddha Samanta, Deepshikha, K. Das · 0 citations

Preprint Sep 2026

Hoffman-type Results for the Sum of k Largest Eigenvalues of a Graph

Let $S_k(G)$ denote the sum of the $k$ largest eigenvalues of a graph $G$. Motivated by the classical Hoffman program for the spectral radius of a graph, we investigate an additive Hoffman-type problem for $S_k(G)$. For each fixed $k\geq 2$ and sufficiently large order $n$, we characterize all connected graphs satisfyi...

Shao-Wei Sun, Meng-Yao Guo, Hong-Yan Ge et al. · 0 citations