let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

In machine learning, a popular tool to analyze the structure of graphs is the hitting time and the commute distance (resistance distance). For two vertices u and v, the hitting time Huv is the expected time it takes a random walk to travel from u to v. The commute distance is its symmetrized version Cuv = Huv +Hvu. In our paper we study the behavior of hitting times and commute distances when t...

A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...

We propose an approach to image retrieval that does not require any distance computations. The idea is to represent images and corresponding image features by means of the two sets of vertices of a bipartite graph. Even though in such a graph the images are not directly related, the degrees to which the features are present in an image allow for defining partial orders. If the degrees of presen...

A tree t-spanner of a graph G is a spanning tree of G such that the distance between pairs of vertices in the tree is at most t times their distance in G. Deciding tree t-spanner admissible graphs has been proved to be tractable for t < 3 and NP-complete for t > 3, while the complexity status of this problem is unresolved when t = 3. For every t > 2 and b > 0, an efficient dynamic programming a...

Article history: Received 22 May 2014 Accepted 8 November 2014 Available online 25 November 2014 Submitted by J.M. Landsberg MSC: 15B99 13P25 20G20

LDPC codes of columnweight of two are constructed fromminimal distance graphs or cages. Distance graphs are used to represent LDPC code matrices such that graph vertices that represent rows and edges are columns. The conversion of a distance graph into matrix form produces an adjacency matrix with column weight of two and girth double that of the graph. The number of 1’s in each row (row weight...

Recent work has found that the propagation of behaviors and sentiments through networks extends in ranges up to 2 to 4 degrees of distance. The regularity with which the same observation is found in dissimilar phenomena has been associated with friction in the propagation process and the instability of link structure that emerges in the dynamic of social networks. We study a contagious behavior...