Steiner Degree Distance of Two Graph Products
نویسندگان
چکیده
منابع مشابه
steiner wiener index of graph products
the wiener index $w(g)$ of a connected graph $g$ is defined as $w(g)=sum_{u,vin v(g)}d_g(u,v)$ where $d_g(u,v)$ is the distance between the vertices $u$ and $v$ of $g$. for $ssubseteq v(g)$, the {it 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 {it $k$-th steiner wiener index/} $sw_k(g)$ of $g$ ...
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the reciprocal degree distance (rdd), defined for a connected graph $g$ as vertex-degree-weighted sum of the reciprocal distances, that is, $rdd(g) =sumlimits_{u,vin v(g)}frac{d_g(u) + d_g(v)}{d_g(u,v)}.$ the reciprocal degree distance is a weight version of the harary index, just as the degree distance is a weight version of the wiener index. in this paper, we present exact formu...
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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 expressi...
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The Steiner distance of a graph, introduced by Chartrand, Oellermann, Tian and Zou in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $Ssubseteq V(G)$, the Steiner distance $d(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. Let $...
متن کاملOn the degree distance of a graph
If G is a connected graph with vertex set V , then the degree distance of G, D′(G), is defined as ∑ {u,v}⊆V (deg u + deg v) d(u, v), where degw is the degree of vertex w, and d(u, v) denotes the distance between u and v. We prove the asymptotically sharp upper bound D′(G) ≤ 14 nd(n− d) 2 +O(n7/2) for graphs of order n and diameter d. As a corollary we obtain the bound D′(G) ≤ 1 27 n 4 + O(n7/2)...
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ژورنال
عنوان ژورنال: Analele Universitatii "Ovidius" Constanta - Seria Matematica
سال: 2019
ISSN: 1844-0835
DOI: 10.2478/auom-2019-0020