On Harary Matrix, Harary Index and Harary Energy
نویسندگان
چکیده
Recently, a new molecular graph matrix, Harary matrix, was defined in honor of Professor Frank Harary, and new graph invariants (local and global) based on it were also defined and researched, Harary index is one of these invariants. The Harary matrix can be used to derive a variant of the Balaban index, Harary index was also successfully tested in several structure-property relationships, so it is very meaningful to research their mathematical properties and chemical applications. As a class of graph energy, Harary energy was introduced not long ago. In this paper, we obtain some results about eigenvalues of Harary matrix, then by these results, we get some bounds of Harary index. Moreover, we obtain some bounds of Harary energy.
منابع مشابه
Nordhaus-Gaddum type results for the Harary index of graphs
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...
متن کاملThree-center Harary index and its applications
The Harary index H can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. A generalization of the Harary index, denoted by Hk, is achieved by employing the Steiner-type distance between k-tuples of atoms. We show that the linear c...
متن کاملExtremal Unicyclic and Bicyclic Graphs with Respect to Harary Index
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, we determined the extremal (maximal and minimal) unicyclic and bicyclic graphs with respect to Harary index. 2010 Mathematics Subject Classification: 05C90
متن کاملHarary Index of Zigzag Polyhex Nanotorus
One of considerable topics in chemistry is surveying the quantitative structure-property relationship between the structure of a molecule and chemical, physical and biological properties of it(QSPR). For this purpose, the form of molecule must be coded according to numbers. A common method, for coding the molecule structure, is to assign a graph to the molecule, where the vertices are atoms of ...
متن کاملHarary index of product graphs
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , whereKm0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for th...
متن کامل