Filomat 2012 Volume 26, Issue 6, Pages: 1189-1200
https://doi.org/10.2298/FIL1206189L
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Cited by
Sharp bounds on Zagreb indices of cacti with k pendant vertices
Li Shuchao (Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, P.R. China)
Yang Huangxu (Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, P.R. China)
Zhao Qin (Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, P.R. China)
For a (molecular) graph, the first Zagreb index M1 is equal to the sum of
squares of its vertex degrees, and the second Zagreb index M2 is equal to the
sum of products of degrees of pairs of adjacent vertices. A connected graph G
is a cactus if any two of its cycles have at most one common vertex. In this
paper, we investigate the first and the second Zagreb indices of cacti with k
pendant vertices. We determine sharp bounds for M1 -, M2 -values of n-vertex
cacti with k pendant vertices. As a consequence, we determine the n-vertex
cacti with maximal Zagreb indices and we also determine the cactus with a
perfect matching having maximal Zagreb indices.
Keywords: Zagreb indices, Cactus graphs, Pendant vertex