Some Relations between Rank, Chromatic Number and Energy of Graphs
| dc.creator | Akbari, S. | |
| dc.creator | Ghorbani, E. | |
| dc.creator | Zare, S. | |
| dc.date | 2007-09-20 | |
| dc.date.accessioned | 2026-07-07T08:31:00Z | |
| dc.date.available | 2026-07-07T08:31:00Z | |
| dc.description | The energy of a graph $G$, denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of $G$. Let $G$ be a graph of order $n$ and ${\rm rank}(G)$ be the rank of the adjacency matrix of $G$. In this paper we characterize all graphs with $E(G)={\rm rank}(G)$. Among other results we show that apart from a few families of graphs, $E(G)\geq 2\max(χ(G), n-χ(\bar{G}))$, where $n$ is the number of vertices of $G$, $\bar{G}$ and $χ(G)$ are the complement and the chromatic number of $G$, respectively. Moreover some new lower bounds for $E(G)$ in terms of ${\rm rank}(G)$ are given. | |
| dc.description | Accepted for publication in Discrete Mathematics | |
| dc.identifier | https://arxiv.org/abs/0709.3140 | |
| dc.identifier | http://arxiv.org/abs/0709.3140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138391 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C15, 05C50, 15A03 | |
| dc.title | Some Relations between Rank, Chromatic Number and Energy of Graphs | |
| dc.type | text |