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On the maximum and minimum first reformulated Zagreb index of graphs with connectivity at most k

Su Guifu (Department of Mathematics, Beijing Institute of Technology, Beijing, P. R. China)
Xiong Liming (Department of Mathematics, Beijing Institute of Technology, Beijing, P. R. China)
Xu Lan (Department of Mathematics, Changji University, Xinjiang, P. R. China)
Ma Beibei (Department of Mathematics, Xinjiang University, Xinjiang, P. R. China)

The authors Miličević et al. introduced the reformulated Zagreb indices [1], which is a generalization of classical Zagreb indices of chemical graph theory. In this paper, we mainly consider the maximum and minimum for the first reformulated index of graphs with connectivity at most k. The corresponding extremal graphs are characterized.

Keywords: the first reformulated Zagreb index, connectivity, maximum and minimum