A star-factor of a graph G is a spanning subgraph of G such that each component of which is a star. Recently, Hartnell and Rall studied a family U of graphs satisfying the property that every star-factor of a member graph has the same number of edges. They determined the family U when the girth is at least five. In this paper, we investigate the family of graphs with girth three and determine a...

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N -fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K2 graphs (Complete graph with two vertices) and the probability of observing wal...

The star graph has been recognized as an attractive alternative to the hypercube. Let Fe and Fv be the sets of vertex faults and edge faults, respectively. Previously, Tseng et al. showed that an n-dimensional star graph can embed a ring of length n! if |Fe |≤n-3 (|Fv|=0), and a ring of length at least n!-4|Fv | if |Fv |≤n-3 (|Fe |=0). Since an n-dimensional star graph is regular of degree n-1 ...

Regular trees can he detined by two types of rational exprwions. For these two types w;isolve the star-height problem, i.e., we show how to construct a rational expression of minimal star-height from the minimal graph of the given tree (i.e., the analogue of the minimal deterministic automaton for regular languages). In one case, the minimal starheight is the rank (in the Sense of Eggan) of the...

Recent work of Lazarovich provides necessary and sufficient conditions on a graph L for there to exist a unique simply-connected (k, L)-complex. The two conditions are symmetry properties of the graph, namely star-transitivity and st(edge)-transitivity. In this paper we investigate star-transitive and st(edge)-transitive graphs by studying the structure of the vertex and edge stabilisers of suc...

We study the urban-scale macroscopic traffic flow in city networks. Star graph is considered as network. graphs with controlled are transformed to various cell-transmission by using cell transmission method. The dynamic equations of vehicular densities on all nodes (roads) presented speed-matching model. density given nonlinear-diffusion equations. star mapped nonlinear diffusion process graphs...