On the Trees with Given Matching Number and the Modified First Zagreb Connection Index

Document Type : Research Paper


1 Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, Pakistan

2 Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, Pakistan


The modified first Zagreb connection index ZC1 for a graph G is defined as ZC1 (G) = \sum v∈V (G) dvτv , where dv is the degree of the vertex v and τv denotes the connection number of v (that is, the number of vertices at the distance 2 from the vertex v). Let Tn,α be the class of trees with order n and matching number α such that n > 2α−1. In this paper, we obtain the lower bounds on the modified first Zagreb connection index of trees belonging to the class Tn,α, for 2α − 1 < n < 3α + 2.


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