A graph is distance-hereditary if for any pair of vertices, their distance in every connected induced subgraph containing both vertices is the same as their distance in the original graph. Distance hereditary graphs are exactly the graphs with rank-width at most 1. The Distance-Hereditary Vertex Deletion problem asks, given a graph G on n vertices and an integer k, whether there is a set S of a...

We give a bound on the sizes of two sets of vertices at a given minimum distance in a graph in terms of polynomials and the Laplace spectrum of the graph. We obtain explicit bounds on the number of vertices at maximal distance and distance two from a given vertex, and on the size of two equally large sets at maximal distance. For graphs with four eigenvalues we find bounds on the number of vert...

Let G = (V, E) be a simple connected graph. The geodesic distance between two vertices u, v in is the length terms of number edges shortest path vertices. In this paper, we determine Gd-distance wreath product graphs. Using formulae obtained here, have found exact value some classes

We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...

A graph X is said to be distance–balanced if for any edge uv of X , the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. A graph X is said to be strongly distance–balanced if for any edge uv of X and any integer k, the number of vertices at distance k from u and at distance k+1 from v is equal to the number of vertices at distance k + 1 from u a...

We consider a random graph process analogous to one suggested by Barabási and Albert. Their model can be roughly described as follows. At each step we add one vertex and one outgoing edge, and the probability that the new vertex is connected to a vertex v is proportional to the degree of v. These types of processes serve as models of real-world networks. In this paper we consider a well-known g...

In this note, we present two lower bounds for the spectral radius of the Laplacian matrices of triangle-free graphs. One is in terms of the numbers of edges and vertices of graphs, and the other is in terms of degrees and average 2-degrees of vertices. We also obtain some other related results.

The excess enthalpy flames and their dynamics below the flammability limit are studied by considering two flames that propagate in opposite directions in parallel channels. The model enables the coupling between the external heat loss, convection preheating, diffusion transport and finite rate chemistry. Analytical expressions for the flame temperature, separation distance, and extinction limit...

While there has been much research on the study of global virtual teams and global software teams, there has been practically no research on the nuances of time separation. We present three converging perspectives on this topic: (1) a view from practices and tactics of global teams; (2) a theoretical view from coordination theories; and (3) a view from our prior research in which we modeled coo...