[PDF] Top 20 Some Results of Resistance Distance and Kirchhoff Index Based on R-Graph

... effective resistance between them when unit resistors are placed on every edge of ...The Kirchhoff index Kf (G) is the sum of resistance distances between all pairs of vertices of ...the ... See full document

... of resistance distance and Kirchhoff index is a hot topic in mathematics, computer science and so ...find some techniques to compute the resistance ... See full document

... the resistance distance between two arbitrary vertices in an electrical network can be obtained in terms of the eigenvalues and eigenvectors of the combinato- rial Laplacian matrix and the normalized ... See full document

... Wiener index is one of the oldest molecular-graph-based structure- ...Wiener index is one of the current areas of research in mathematical ...Wiener index (of molecular graphs) and the ... See full document

... Bu, Some results on Kirchhoff index and degree– Kirchhoff index, MATCH ...Randi'c, Resistance distance, ... See full document

... of some complicated chemical ...degree based indices and distance based ...known graph structure in Chemical graph ...Zagreb index of some graph operations ... See full document

... approach based on classical molecular mechanics to accounting for small displacements of atoms from their equilibrium positions due to oscillations or ...the Kirchhoff index as well as of the Wiener ... See full document

... matrix X such that MXM = M, XMX = X and MX = XM. It is known that M # exists if and only if rank ( M ) = rank ( M 2 ) ([17],[18]). If M is real symmetric, then M # exists and M # is a symmetric { 1 } -inverse of M. ... See full document

... connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is ...k. Some formulas are obtained for computing the ... See full document

... connected graph, and let D[G] denote the double graph of ...for some distance based topological indices for D[G ] in terms of ...complete graph, the path and the ... See full document

... Exploiting the strong connection between random walks and effective resis- tance, an outline of this connection is given in Sections 2.2 & 2.5, we can apply our bounds on resistance to a number of random walk ... See full document

... Example 3.1. Consider the carbon nanocones CNC 3 ( 1 ) shown in Figure 3. This molecular structure has 15 edges, where three of them with s ( u ) = s ( v ) = 5, six of them with s ( u ) = 7 and s ( v ) = 5, three of them ... See full document

... as graph database D. To speed up query answering on graph databases, indexes are commonly ...State-of-the-art graph database indexes do not adapt or scale well to dynamic graph database use; ... See full document

... connected graph with vertex and edge set, V(G) and E(G), respectively. The distance between the vertices u and v of G is denoted by d(u,v) and defined as the number of edges in a minimal path connecting the ... See full document

... adjacent to some vertex in . S The domination number of G denoted by γ (G ) is the minimal cardinality taken over all dominating sets of G A subset F of E is called an . edge dominating set if each edge in E is ... See full document

... Definition−1.1 : A function f : V (G) −→ {0, 1} is called a binary vertex labeling of a graph G and f(v) is called label of the vertex v of G under f. The induced func- tion f ∗ : E(G) −→ {0, 1} is defined as f ∗ ... See full document

... vertex distance gets the maximum at the vertex (the center) with the maximum vertex-degree and the minimum at the vertex (the leaf) with the smallest ...These results reveal that the distribution of the ... See full document

... the graph representation of objects in each frame, with regard that the first frame is the initial state and the algorithm dos not calculate the features for this ... See full document

... connected graph with n vertices and m edges, with vertex set V(G) = {1,2,…,n} and edge set ...the distance d(x,y|G) between two vertices x, y  V(G) is defined as the length (= number of edges) of the ... See full document

... be r-complete if every vertex in V(G) is r-adjacent to every other vertex in V(G) ...is r-complete is called r-clique number of G and is denoted by  r ...Let r ≥ 1. Let u ,v  ... See full document