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...

A mixed graph D is a that can be obtained from by orienting some of its edges. Let α primitive n th root unity, then the α−Hermitian adjacency matrix defined to Hα = [hrs] where hrs if rs an arc in D, sr 1 digon and 0 otherwise. In this paper we study cospectrality Hermitian graph.

In th is pap er w e prop ose a hybrid g en etic a lgo­ rith m for th e graph b alanced b i-p a rtition prob lem , a chal­ len g in g N P -h ard com b in atoria l o p tim iza tio n prob lem aris­ ing in m any p ractica l ap p lica tion s. T h e hybrid character o f th e G A lies in th e ap p lica tion o f a h eu ristic p rocedu re to im prove can d id ate so lu tion s. T h e b asic idea b eh in ...

A graph G is convergent when there is some nite integer n 0, such that the n-th iterated clique graph K n (G) has only one vertex. The smallest such n is the index of G. The Helly defect of a convergent graph is the smallest n such that K n (G) is clique Helly, that is, its maximal cliques satisfy the Helly property. Bandelt and Prisner proved that the Helly defect of a chordal graph is at most...

We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an exponentially small additive error in classical polynomial time. First, we show that there exists a commuting quantum circuit that is not classically simulatable unles...

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...