We construct canonical quantum fields which propagate on a star graph modeling a quantum wire. The construction uses a deformation of the algebra of canonical commutation relations, encoding the interaction in the vertex of the graph. We discuss in this framework the Casimir effect and derive the correction to the Stefan-Boltzmann law induced by the vertex interaction. We also generalize the al...

The terminal matrix is the distance matrix between all pairs of valence one vertices of a given graph and the terminal polynomial is the characteristic polynomial of the terminal matrix. Star-like graphs are connected graphs with at most one vertex of degree 3 d  . The recursive formula that calculates the terminal polynomial of a star-like graph is given. Particularly, the formula that calcul...

In this paper, we prove that the square graph of bistar Bn,n, the splitting graph of Bn,n and the splitting graph of star K1,n are graceful graphs. We also prove that the splitting graph and the shadow graph of bistar Bn,n admit odd graceful labeling.

Given a plane graph, a k-star at u is a set of k vertices with a common neighbour u; and a bunch is a maximal collection of paths of length at most two in the graph, such that all paths have the same end vertices and the edges of the paths form consecutive edges ( in the natural order in the plane graph ) around the two end vertices. We prove a theorem on the structure of plane triangulations i...

Multicast is an important collective communication operation on multicomputer systems, in which the same message is delivered from a source node to an arbitrary number of destination nodes. The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In our previous work on wormhole star graph networks routing, we proposed a path-base...

Given a plane graph, a k-star at u is a set of k vertices with a common neighbour u; and a bunch is a maximal collection of paths of length at most two in the graph, such that all paths have the same end vertices and the edges of the paths form consecutive edges ( in the natural order in the plane graph ) around the two end vertices. We first prove a theorem on the structure of plane graphs in ...

The star graph S n is a graph with S n the set of all permutations over f1; : : :; ng as its vertex set; two vertices 1 and 2 are connected if 1 can be obtained form 2 by swapping the rst element of 1 with one of the other n ? 1 elements. In this paper we establish the genus of the star graph. We show that the genus, g n of S n , is exactly equal to n!(n?4)=6+1 by establishing a lower bound and...

Let G(v, e) be the set of all simple graphs with v vertices and e edges and let P2(G) = ∑ di denote the sum of the squares of the degrees, d1, . . . , dv, of the vertices of G. It is known that the maximum value of P2(G) for G ∈ G(v, e) occurs at one or both of two special graphs in G(v, e)—the quasi-star graph or the quasi-complete graph. For each pair (v, e), we determine which of these two g...

Let G(v, e) be the set of all simple graphs with v vertices and e edges and let P2(G) = ∑ d i denote the sum of the squares of the degrees, d1, . . . , dv, of the vertices of G. It is known that the maximum value of P2(G) for G ∈ G(v, e) occurs at one or both of two special graphs in G(v, e)—the quasi-star graph or the quasi-complete graph. For each pair (v, e), we determine which of these two ...

—We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N 3 /n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N ≥ (n-1)!. The incurred communication time is better than the best known results for the hyp...