The single-vertex union of Cm,Cn and Cl is homeomorphic to the bouquets of circles B3 consisting of 3 self-loops.In the paper,from the perspective of using graph invariants to describe the topological property of complex networks quantitatively,we firstly use the method of classified discussion and present the vertex Gutman index on B3.Secondly,we study the maximum and minimum of vertex Gutman index on each partition circle and B3,respectively.Finally,we obtain the formula of vertex Gutman index on Bn(n ≥ 4)by generalizing the result of B3.The results show that the maximum of the vertex Gutman index on the split circle is obtained at the farthest distance from the center,the maximum of the vertex Gutman index on the bouquets of circles is always obtained at the center,and the minimum are all obtained at some vertices closest to the center.
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