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A characterization of graphs with rank 4 |
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| Authors: | Gerard J Chang Liang-Hao Huang Hong-Gwa Yeh |
| Institution: | a Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan b Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan c National Center for Theoretical Sciences, Taipei Office, Taiwan d Department of Mathematics, National Central University, Jhongli City, Taoyuan 32001, Taiwan |
| 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 with rank 4? This question has not yet been fully answered in the literature, and only some partial results are known. In this paper we resolve this question by completely characterizing graphs G whose adjacency matrix has rank 4. |
| Keywords: | 05C50 15A18 05C75 05C76 |
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