For a graph G, vertex v of G and integer r ≥ 1, we denote the family of independent r-sets of V (G) by I(r)(G) and the subfamily {A ∈ I(r)(G) : v ∈ A} by I v (G); such a subfamily is called a star. Then, G is said to be r-EKR if no intersecting subfamily of I(r)(G) is larger than the largest star in I(r)(G). If every intersecting subfamily of I v (G) of maximum size is a star, then G is said to...

A hyper-star graph HS(n,k) provides a promising topology for interconnection networks of parallel processing systems because it inherits the advantages of a hypercube and a star graph. In this paper, we focus on fault-tolerant routing in an HS(n,k) graph with faulty nodes and propose an algorithm to establish a fault-free path between a pair of non-faulty nodes. The algorithm uses limited globa...

We study the stochastic birth-death model for structured finite populations popularized by Lieberman et al. [Lieberman, E., Hauert, C., Nowak, M.A., 2005. Evolutionary dynamics on graphs. Nature 433, 312-316]. We consider all possible connected undirected graphs of orders three through eight. For each graph, using the Monte Carlo Markov Chain simulations, we determine the fixation probability o...

Perhaps the most widely appreciated linked data principle is the one that instructs linked data providers to provide useful information using the standards (i.e., RDF and SPARQL). Such information corresponds to patterns expressed as SPARQL queries that are matched against the RDF graph. Until recently, it was not possible to create a pattern without specifying the exact path that would match a...

A group of mobile robots can localize cooperatively, using relative position and absolute orientation measurements, fused through an extended Kalman filter (ekf). The topology of the graph of relative measurements is known to affect the steady state value of the position error covariance matrix. Classes of sensor graphs are identified, for which tight bounds for the trace of the covariance matr...

Clustering is the unsupervised process of discovering natural clusters so that objects within the same cluster are similar and objects from different clusters are dissimilar. In clustering, if similarity relations between objects are represented as a simple, weighted graph where objects are vertices and similarities between objects are weights of edges; clustering reduces to the problem of grap...

For a graph G and any two vertices u and v in G, let d(u, v) denote the distance between u and v and let diam(G) be the diameter of G. A multilevel distance labeling (or radio labeling) for G is a function f that assigns to each vertex of G a positive integer such that for any two distinct vertices u and v, d(u, v)+ | f(u) − f(v) |≥ diam(G) + 1. The largest integer in the range of f is called t...

A graph G is called a pairwise compatibility graph (PCG, for short) if it admits a tuple (T,w, dmin, dmax) of a tree T whose leaf set is equal to the vertex set of G, a non-negative edge weight w, and two non-negative reals dmin ≤ dmax such that G has an edge between two vertices u, v ∈ V if and only if the distance between the two leaves u and v in the weighted tree (T, w) is in the interval [...

If G is a maximal exceptional graph then either (a) G is the cone over a graph switching-equivalent to the line graph L(K8) or (b) G has K8 as a star complement for the eigenvalue −2 (or both). In case (b) it is shown how G can be constructed from K8 using intersecting families of 3-sets.

An asteroidal triple in a graph is a set of three non-adjacent vertices such that for any two of them there exists a path between them that does not intersect the neighborhood of the third. An asteroidal quadruple is a set of four non-adjacent vertices such that any three of them is an asteroidal triple. In this paper, we study a subclass of directed path graph, the class of extended star direc...