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A note on ABC spectral radii of unicyclic graphs
  • Yan Yuan
Yan Yuan
South China Normal University

Corresponding Author:[email protected]

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The ABC spectral radius of a graph G is the largest eigenvalue of the ABC matrix modified from the adjacency matrix of G so that the (u,v)-entry is √(du+dv-2)/√dudv for an edge uv, where dw is the degree of vertex w in G. We show that the graph formed from a cycle of length n-p by attaching p pendent edges to a vertex uniquely maximizes the ABC spectral radius over all n-vertex unicyclic graphs with p pendant edges, and over all n-vertex unicyclic graphs with girth n-p, respectively.