On the harmonic index and the matching number of a tree
نویسندگان
چکیده
The harmonic index of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we give a sharp lower bound on the harmonic index of trees with a perfect matching in terms of the number of vertices. A sharp lower bound on the harmonic index of trees with a given size of matching is also obtained.
منابع مشابه
The augmented Zagreb index, vertex connectivity and matching number of graphs
Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
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عنوان ژورنال:
- Ars Comb.
دوره 116 شماره
صفحات -
تاریخ انتشار 2014