The nullity of (k-1)-cyclic graphs☆

@inproceedings{Tan2013TheNO,
  title={The nullity of (k-1)-cyclic graphs☆},
  author={Xuezhong Tan and Bolian Liu},
  year={2013}
}
Abstract A simple connected graph is called a k - cyclic graph provided that the number of edges equals its order plus ( k - 1 ) . In this paper, we define a class of ( k - 1 ) -cyclic graph, denoted by Θ k . The singularity of Θ-graph is studied. Also, the ( k - 1 ) -cyclic graphs that contain Θ-graph as an induced subgraph are paid much attention. We characterize those graphs that have extreme nullities. The results generalize the corresponding theorems on unicyclic and bicyclic graphs. 

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