In 1996, Ota and Tokuda showed that a star-free graph with sufficiently high minimum degree admits a 2-factor. More recently it was shown that the minimum degree condition can be significantly reduced if one also requires that the graph is not only star-free but also of sufficiently high edge-connectivity. In this paper we reduce the minimum degree condition further for star-free graphs that al...

<p>A graph denoted by is a pair of where non-empty set vertices in G, and E edges G. In theory, there are various types graphs including star graphs, cycle graph, wheel graph. Graph operations on two or more can produce new graphs. Amalgamation one the Suppose connected amalgamating 1 2 joining obtained joins vertex into , common resulting from while edge combining g, g side (

Abstmcr-The n-star graph, denoted by S,, is one of the graph networks that have been recently proposed as attractive alternatives to the n-cube topology for interconnecting processors in parallel computers. In this paper, we present a parallel algorithm for the computation of the Fourier transform on the star graph. The algorithm requires O(n*)multiply-add steps for an input sequence of n! elem...

A directed star forest is a forest all of whose components are stars with arcs emanating from the center to the leaves. The acircuitic directed star arboricity of an oriented graph G (that is a digraph with no opposite arcs) is the minimum number of edge-disjoint directed star forests whose union covers all edges of G and such that the union of any two such forests is acircuitic. We show that e...

Let G be a connected graph with least eigenvalue −2, of multiplicity k. A star complement for −2 in G is an induced subgraph H = G − X such that |X | = k and −2 is not an eigenvalue of H . In the case that G is a generalized line graph, a characterization of such subgraphs is used to decribe the eigenspace of −2. In some instances, G itself can be characterized by a star complement. If G is not...

A double-star is a tree with exactly two vertices of degree greater than 1. If T is a double-star where the two vertices of degree greater than one have degrees k1+1 and k2+1, then T is denoted by Sk1,k2 . In this note, we show that every double-star with n edges decomposes every 2n-regular graph. We also show that the double-star Sk,k−1 decomposes every 2k-regular graph that contains a perfect...

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The generalized (n, k)-star graph was introduced to address scaling issues of the star graph, and it has many de...

The (n, k)-star graph is a generalization of the n-star graph. It has better scalability than the n-star graph and holds some good properties compared with the hypercube. This paper focuses on the design of the fault-tolerant routing algorithm for the (n, k)-star graph. We adopt the idea of collecting the limited global information used for routing on the n-star graph to the (n, k)-star graph. ...