نتایج جستجو برای: randić index

تعداد نتایج: 396100  

Journal: :iranian journal of mathematical chemistry 2013
y. alizadeh

let g be a simple graph with vertex set v(g) {v1,v2 ,...vn} . for every vertex i v , ( ) i  vrepresents the degree of vertex i v . the h-th order of randić index, h r is defined as the sumof terms1 2 11( ), ( )... ( ) i i ih  v  v  vover all paths of length h contained (as sub graphs) in g . inthis paper , some bounds for higher randić index and a method for computing the higherrandic ind...

2007
Xueliang Li Yongtang Shi

The general Randić index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real number, which is called the Randić index or connectivity index (or branching index) for α = −1/2 proposed by Milan Randić in 1975. The paper outlines the results known for the (general) Randić inde...

2012
JIANPING LI BO ZHOU B. ZHOU

The modified Randić index of a graph G is a graph invariant closely related to the classical Randić index, defined as

2017
Süleyman Ediz

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph....

2006
Huiqing Liu Xiangfeng Pan Jun-Ming Xu

The Randić index R(G) of a graph G is the sum of the weights (d(u)d(v))− 1 2 of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we first present a sharp lower bound on the Randić index of conjugated unicyclic graphs (unicyclic graphs with perfect matching). Also a sharp lower bound on the Randić index of unicyclic graphs is given in terms of the order and given ...

2005
Huiqing LIU Mei LU Feng TIAN

The general Randić index of an organic molecule whose molecular graph is G is defined as the sum of (d(u)d(v))α over all pairs of adjacent vertices of G, where d(u) is the degree of the vertex u in G and α is a real number with α 6= 0. In the paper, we obtained sharp bounds on the general Randić index of the Nordhaus-Gaddum type for trees. Also we show that the general Randić index of the Nordh...

2010
Jianguang Yang Fangli Xia Shubo Chen S. Chen

The Randić index R(G) of an organic molecule whose molecular graph is G is the sum of the weights (dudv)− 1 2 of all edges uv of G, where du(or dv) denote the degree of vertex u(or v). Efficient formulas for calculating the Randić index of polyomino chains are provided. Mathematics Subject Classification: 05C50, 05C12, 05C05

Journal: :CoRR 2013
Sarah J. Kunkler Michael Drew Lamar Rex K. Kincaid David Phillips

We show that finding a graph realization with the minimum Randić index for a given degree sequence is solvable in polynomial time by formulating the problem as a minimum weight perfect b-matching problem. However, the realization found via this reduction is not guaranteed to be connected. Approximating the minimum weight b-matching problem subject to a connectivity constraint is shown to be NP-...

Journal: :iranian journal of mathematical chemistry 2015
m. a. iranmanesh m. saheli

the harmonic index h(g) , of a graph g is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in e(g), where deg (u) denotes the degree of a vertex u in v(g). in this paper we define the harmonic polynomial of g. we present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in caterpill...

Journal: :Networks 2016
Rex K. Kincaid Sarah J. Kunkler Michael Drew Lamar David Phillips

We show that finding a subgraph realization with the minimum generalized Randić index for a given base graph and degree sequence is solvable in polynomial time by formulating the problem as the minimum weight perfect b-matching problem of Edmonds (J Res Natl Bur Stand 69B (1965), 125–130). However, the realization found via this reduction is not guaranteed to be connected. Approximating the min...

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