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...

Star-ladder graphs were introduced by Gross in his development of a quadratic-time algorithm for the genus distribution of a cubic outerplanar graph. This paper derives a formula for the genus distribution of star-ladder graphs, using Mohar’s overlap matrix and Chebyshev polynomials. Newly developed methods have led to a number of recent papers that derive genus distributions and total embeddin...

Let G be a graph and f : V (G) → {2, 3, . . .}. A spanning subgraph F is called strong f -star of G if each component of F is a star whose center x satisfies degF (x) ≤ f(x) and F is an induced subgraph of G. In this paper, we prove that G has a strong f -star factor if and only if oddca(G − S) ≤

We present and analyze the o -line star algorithm for clustering static information systems and the online star algorithm for clustering dynamic information systems. These algorithms partition a document collection into a number of clusters that is naturally induced by the collection. We show a lower bound on the accuracy of the clusters produced by these algorithms. We use the random graph mod...

We consider the Moran process in a graph called “star” and obtain the asymptotic expression for the fixation probability of a single mutant when the size of the graph is large. The expression obtained corrects previously known expression announced in reference [E Lieberman, C Hauert, and MA Nowak. Evolutionary dynamics on graphs. Nature, 433(7023):312–316, 2005] and further studied in [M. Broom...

We construct an action of a braid group associated to a complete graph on the derived category of a certain symmetric Nakayama algebra which is also a Brauer star algebra with no exceptional vertex. We connect this action with the affine braid group action on Brauer star algebras defined by Schaps and Zakay-Illouz. We show that for Brauer star algebras with no exceptional vertex, the action is ...

star identification is one of the most important stages in attitude determination with star trackers. this can be performed using matching algorithms between observed stars and a master star catalogue. the main challenge in this approach is to provide a fast and reliable identification algorithm that is sufficiently robust in different pointing views of the star tracker optical system in the sp...

In earlier work [LMP11], we showed that a graph-theoretic condition called “structural cyclicity” enables us to extract syntax from a conflict-equivalent product system of automata. In this paper we have a “pairing” property in our syntax which allows us to connect to a broader class of product systems, where the conflict-equivalence is not statically fixed. These systems have been related to l...

We prove lower and upper bounds on bisection widths of the transposition graphs. This class of graphs contains several frequently studied interconnection networks including star graphs and hypercubes. In particular, we prove that the bisection width of the complete transposition graph is of order (n:n!) which solves the open problem (R) 3.356 of the Leighton's book 11] and determine nearly exac...

In this paper, we consider the fault Hamiltonicity, and the fault Hamiltonian connectivity of the (n, k)-star graph Sn,k. Assume that F V(Sn,k) E(Sn,k). For n k ≥ 2, we prove that Sn,k F is Hamiltonian if F ≤ n 3 and Sn,k F is Hamiltonian connected if F ≤ n 4. For n k 1, Sn,n 1 is isomorphic to the n-star graph Sn which is known to be Hamiltonian if and only if n > 2 and Hamiltonian connected i...