The continuous-time quantum walk (CTQW) on root lattice An ( known as hexagonal lattice for n = 2) and honeycomb one is investigated by using spectral distribution method. To this aim, some association schemes are constructed from abelian group Z⊗n m and two copies of finite hexagonal lattices, such that their underlying graphs tend to root lattice An and honeycomb one, as the size of the under...

We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent results of [10] that were proved for graphs with bounded chromatic number and with symmetric coupling distribution. Furthermore, we generalise the result to arbitr...

In this paper, we define the non-centralizer graph associated to a finite group G, as the graph whose vertices are the elements of G, and whose edges are obtained by joining two distinct vertices if their centralizers are not equal. We denote this graph by ΥG. The non-centralizer graph is used to study the properties of the non-commuting graph of an AC-group. We prove that the non-centralizer g...

The aim of this paper is to study the Wold-type decomposition in class $m$-isometries. One our main results establishes an equivalent condition for analytic $m$-isometry admit $m\ge2$. In particular, we introduce $k$-kernel which use characterize $m$-isometric operators are unitarily unilateral operator valued weighted shifts As a result, also show that composition on directed graphs with one c...

We establish the tracial stability of a certain class graph products C*-algebras. This result involves development pincushion finite graphs. then apply this in two ways. The first application yields selective version Lin's Theorem for almost commuting operators. second addresses some approximation properties right-angled Artin groups. In particular, we show that full C*-algebra any group is qua...

Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras, whose coalgebra parts are not necessarily coassociative. Similarly, certain algebraic descriptions of combinatorial objects such as weighted directed graphs through a coalgebraic formulation often require at least two coalgebras whose cop...

In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [−1− √ 2,−2) and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [α1,−1− √ 2) where α1 is the smallest root(≈ −2.4812) of the polynomial x3 + 2x2 − 2x − 2. From these results, we ...

iv Acknowledgements v List of Tables vii List of Graphs vii

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