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On reformulated Zagreb indices
Authors:Aleksandar Ili?  Bo Zhou
Institution:
  • a Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
  • b Department of Mathematics, South China Normal University, Guangzhou 510631, PR China
  • Abstract:The first and second reformulated Zagreb indices are defined respectively in terms of edge-degrees as EM1(G)=∑eEdeg(e)2 and EM2(G)=∑efdeg(e)deg(f), where deg(e) denotes the degree of the edge e, and ef means that the edges e and f are adjacent. We give upper and lower bounds for the first reformulated Zagreb index, and lower bounds for the second reformulated Zagreb index. Then we determine the extremal n-vertex unicyclic graphs with minimum and maximum first and second Zagreb indices, respectively. Furthermore, we introduce another generalization of Zagreb indices.
    Keywords:Zagreb index  Reformulated Zagreb index  Vertex degrees  Line graph  Unicyclic graph
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