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Some Bounds on Zeroth-Order General Randi\'c$ Index
For a graph without isolated vertices, the inverse degree of a graph
is defined as where is the number of
vertices adjacent to the vertex in . By replacing by any non-zero
real number we obtain zeroth-order general Randi\'c index, i.e.
where is any non-zero
real number. In \cite{xd}, Xu et. al. determined some upper and lower bounds on
the inverse degree for a connected graph in terms of chromatic number,
clique number, connectivity, number of cut edges. In this paper, we extend
their results and investigate if the same results hold for . The
corresponding extremal graphs have been also characterized.Comment: pages 14, Fig.