A characterization of graphs with rank 5

By Gerard Jennhwa Chang, Liang-Hao Huang, Hong-Gwa Yeh. 2012

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Abstract The rank of a graph G is defined to be the rank of its adjacency matrix. In this paper, we consider the following problem: what is the structure of a connected graph G with rank 5? or equivalently, what is the structure of a connected n-vertex graph G whose adjacency matrix has nullity n - 5 ? In this paper, we completely characterize connected graphs G whose adjacency matrix has rank 5.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0e6c78ff1c5c83aa95c255cc3d23656fc6e7f99b