The harmonic index of a graph
نویسندگان
چکیده
منابع مشابه
on the harmonic index of graph operations
the harmonic index of a connected graph $g$, denoted by $h(g)$, is defined as $h(g)=sum_{uvin e(g)}frac{2}{d_u+d_v}$ where $d_v$ is the degree of a vertex $v$ in g. in this paper, expressions for the harary indices of the join, corona product, cartesian product, composition and symmetric difference of graphs are derived.
متن کاملAshwini Index of a Graph
Motivated by the terminal Wiener index, we define the Ashwini index $mathcal{A}$ of trees as begin{eqnarray*} % nonumber to remove numbering (before each equation) mathcal{A}(T) &=& sumlimits_{1leq i
متن کاملNote on the harmonic index of a graph
The harmonic index of a graph G is defined as the sum of weights 2 deg(v)+deg(u) of all edges uv of E(G), where deg(v) denotes the degree of a vertex v in V (G). In this note we generalize results of [L. Zhong, The harmonic index on graphs, Appl. Math. Lett. 25 (2012), 561– 566] and establish some upper and lower bounds on the harmonic index of G.
متن کاملPeripheral Wiener Index of a Graph
The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...
متن کاملOn 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2014
ISSN: 0035-7596
DOI: 10.1216/rmj-2014-44-5-1607