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- W2952202035 abstract "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, $E(G)geq 2max(chi(G), n-chi(bar{G}))$, where $n$ is the number of vertices of $G$, $bar{G}$ and $chi(G)$ 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." @default.
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- W2952202035 date "2007-09-20" @default.
- W2952202035 modified "2023-09-27" @default.
- W2952202035 title "Some Relations between Rank, Chromatic Number and Energy of Graphs" @default.
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