The minimum harmonic index for bicyclic graphs with given diameter
نویسندگان
چکیده
The harmonic index of a graph G, is defined as the sum weights 2/d(u)+d(v) all edges uv where d(u) degree vertex u in G. In this paper we find minimum bicyclic order n and diameter d. We also characterized graphs reaching bound.
منابع مشابه
On the harmonic index of bicyclic graphs
The harmonic index of a graph $G$, denoted by $H(G)$, is defined asthe sum of weights $2/[d(u)+d(v)]$ over all edges $uv$ of $G$, where$d(u)$ denotes the degree of a vertex $u$. Hu and Zhou [Y. Hu and X. Zhou, WSEAS Trans. Math. {bf 12} (2013) 716--726] proved that for any bicyclic graph $G$ of order $ngeq 4$, $H(G)le frac{n}{2}-frac{1}{15}$ and characterize all extremal bicyclic graphs.In this...
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The harmonic index H(G) 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) denotes the degree of a vertex u in G. In this paper, we have determined the minimum and maximum harmonic indices of bicyclic graphs and characterized the corresponding graphs at which the extremal harmonic indices are attained.
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ژورنال
عنوان ژورنال: Filomat
سال: 2022
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2201125a