On the rank (nullity) of a connected graph

11 Mar 2019 Wang Zhiwen Guo Jiming

The rank $r(G)$ of a graph $G$ is the rank of its adjacency matrix $A(G)$ and the nullity $\eta(G)$ of $G$ is the multiplicity of $0$ as an eigenvalue of $A(G)$. In this paper, we prove that if $G$ is a connected graph of order $n$ with rank $r$, then $G$ contains a nonsingular connected induced subgraph of order $r$... (read more)

PDF Abstract
No code implementations yet. Submit your code now

Categories


  • COMBINATORICS