Steiner Wiener Index of Graph Products
نویسندگان
چکیده
The Wiener index W (G) of a connected graph G is defined as W (G) = ∑ u,v∈V (G) dG(u, v) where dG(u, v) is the distance between the vertices u and v of G. For S ⊆ V (G), the Steiner distance d(S) of the vertices of S is the minimum size of a connected subgraph of G whose vertex set is S. The k-th Steiner Wiener index SWk(G) of G is defined as SWk(G) = ∑ S⊆V (G) |S|=k d(S). We establish expressions for the k-th Steiner Wiener index on the join, corona, cluster, lexicographical product, and Cartesian product of graphs.
منابع مشابه
On the Steiner hyper-Wiener index of a graph
For a connected graph G and an non-empty set S ⊆ V (G), the Steiner distance dG(S) among the vertices of S is defined as the minimum size among all connected subgraphs whose vertex sets contain S. This concept represents a natural generalization of the concept of classical graph distance. Recently, the Steiner Wiener index of a graph was introduced by replacing the classical graph distance used...
متن کاملMORE ON EDGE HYPER WIENER INDEX OF GRAPHS
Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). The (first) edge-hyper Wiener index of the graph G is defined as: $$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). In thi...
متن کاملNordhaus-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 کاملWiener Polarity Index of Tensor Product of Graphs
Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index ...
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 کامل