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Hamiltonian properties of Toeplitz graphs

René van Dal, Gert Tijssen, Zsolt Tuza, Jack A.A. van der Veen, Christina Zamfirescu, Tudor Zamfirescu
1996 Discrete Mathematics  
Conditions are given for the existence of hamiltonian paths and cycles in the so-called Toeplitz graphs, i.e. simple graphs with a symmetric Toeplitz adjacency matrix.  ...  Zamfirescu thankfully acknowledges generous support from the University of Groningen in 1990 and from the European Community during the COST mobility action CIPA-CT-93-1547.  ...  Our motivation for considering hamiltonian properties of Toeplitz graphs is twofold.  ... 
doi:10.1016/0012-365x(95)00111-9 fatcat:q44s2y5vmfegldljt7atmj7joe

The Property of Hamiltonian Connectedness in Toeplitz Graphs

Ayesha Shabbir, Muhammad Faisal Nadeem, Tudor Zamfirescu
2020 Complexity  
A graph G is called Hamiltonian-connected if any two vertices of G are connected by a Hamiltonian path. We consider here the family of Toeplitz graphs.  ...  Here, we prove that the nonbipartite Toeplitz graph Tn1,q,r is Hamiltonian-connected for all 1<q<r<n and n≥5r−2.  ...  In this paper, we are investigating this property of Hamiltonian connectedness for some classes of Toeplitz graphs. Let n, t 1 , t 2 , . . . , t k ∈ N such that 1 ≤ t 1 < t 2 < · · · < t k < n.  ... 
doi:10.1155/2020/5608720 fatcat:nkgd6f3xararvlsbyi4u2t5xzi

Page 4714 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
A.; Zamfirescu, Christina (1-CUNYH-C; New York, NY); Zamfirescu, Tudor (D-DORT; Dortmund) Hamiltonian properties of Toeplitz graphs. (English summary) Discrete Math. 159 (1996), no. 1-3, 69-81.  ...  The current paper studies the existence of Hamiltonian paths and cycles in Toeplitz graphs. Let f), f2,---, t, be the diagonals containing ones in the adjacency matrix of a Toeplitz graph.  ... 

Hamiltonian Connectedness of Toeplitz Graphs [chapter]

Muhammad Faisal Nadeem, Ayesha Shabbir, Tudor Zamfirescu
2014 Springer Proceedings in Mathematics & Statistics  
The property of being Hamiltonian connected is stronger than being Hamiltonian.  ...  Therefore, a Toeplitz graph T is uniquely defined by the first row of A.T /, a (0-1) sequence.  ...  Some Hamiltonian properties of undirected Toeplitz graphs have been investigated in [1] and [5] , while the directed case was studied in [6] [7] [8] . In [9] , S. Malik and T.  ... 
doi:10.1007/978-3-0348-0859-0_8 fatcat:itesg2et7fbd5mbn4bojdygayq

On hamiltonian Toeplitz graphs

Clemens Heuberger
2002 Discrete Mathematics  
We consider hamiltonian properties of Toeplitz graphs, i.e. graphs whose adjacency matrix is constant along diagonals. Extending previous results of van Dal et al.  ...  (Discrete Math. 159 (1996) 69) we prove connectivity and Hamiltonicity for some classes of Toeplitz graphs.  ...  Hamiltonian properties of Toeplitz graphs with two stripes In this section we start our studies of hamiltonian properties of Toeplitz graphs with the case m = 2.  ... 
doi:10.1016/s0012-365x(01)00136-4 fatcat:f3iy4ondubae7cvc5w2uikudbe

Page 6010 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
is Hamiltonian if H'E+EH =0.  ...  and ‘o’ denotes the Hadamard product, the monotonicity property dual to that asserted by the generalized Levinger theorem is established.”  ... 

Counting independent sets in Riordan graphs [article]

Gi-Sang Cheon, Ji-Hwan Jung, Bumtle Kang, Hana Kim, Suh-Ryung Kim, Sergey Kitaev, Seyed Ahmad Mojallal
2020 arXiv   pre-print
The notion of a Riordan graph was introduced recently, and it is a far-reaching generalization of the well-known Pascal graphs and Toeplitz graphs.  ...  However, apart from a certain subclass of Toeplitz graphs, nothing was known on independent sets in Riordan graphs.  ...  properties of such sequences).  ... 
arXiv:2006.16579v1 fatcat:fgzf5wrvaza33huoshr6x5fjs4

Page 4034 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
Xiao Feng Guo (PRC-XIAM; Xiamen) 2003f:05077 05C45 Heuberger, Clemens (A-TGRZ-B; Graz On Hamiltonian Toeplitz graphs. (English summary) Discrete Math. 245 (2002), no. 1-3, 107-1235.  ...  G(V,E) = T,(a\, a2 dm) 1s a Toeplitz graph if V = 1} and E = {[i, jJe V?: Sk € {1,2,...,m}: |j—- = a,}.  ... 

Page 3820 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
In this paper, Hamiltonian decompositions of K,,,,— E(U) are found where U is any 2-factor of K,,,,.  ...  Summary: “A Toeplitz graph is a symmetric graph whose adja- cency matrix is Toeplitz. If such a graph has neither loops nor multiple edges it can be defined by a 0-1 sequence. In [R. Euler, H.  ... 

Characterizing bipartite Toeplitz graphs

Reinhardt Euler
2001 Theoretical Computer Science  
A Toeplitz graph is a symmetric graph whose adjacency matrix is Toeplitz. If such a graph has neither loops nor multiple edges it can be deÿned by a 0 -1 sequence. In Euler et al.  ...  .), Combinatorics and Graph Theory '95, vol. 1, Academia Sinica, World Scientiÿc, Singapore, 1995, pp. 119 -130) inÿnite, bipartite Toeplitz graphs have been fully characterized.  ...  These and related questions have been treated only recently and in di erent contexts: connectivity properties have been studied in [6, 1, 2, 10] , and hamiltonian properties in [11, 7, 9, 8] .  ... 
doi:10.1016/s0304-3975(00)00230-9 fatcat:6njt6dsvcjfn3lwsl3gnk6c4ne

Toeplitz algebras and spectral results for the one-dimensional Heisenberg model

Mondher Damak, Marius Măntoiu, Rafael Tiedra de Aldecoa
2006 Journal of Mathematical Physics  
This class contains the Hamiltonian of the one-dimensional Heisenberg model.  ...  We determine the structure of the spectrum and obtain non-propagation estimates for a class of Toeplitz operators acting on a subset of the lattice ^N.  ...  Part of this work has been completed while M. Mȃntoiu visited the University of Geneva; he expresses his gratitude to W. Amrein for his kind hospitality.  ... 
doi:10.1063/1.2222083 fatcat:zsdzrvetlzgjngegmvqckvuakm

Page 5133 of Mathematical Reviews Vol. , Issue 86k [page]

1986 Mathematical Reviews  
Examples are also given of spaces lacking this property.  ...  The domain D of K is a solid ideal of L°(X) and in the graph topology ||u|| = px(u) + py(|K|u), where |K| is the integral transformation with kernel |k|; K is a continuous linear integral transformation  ... 

Riordan graphs I: Structural properties [article]

Gi-Sang Cheon, Ji-Hwan Jung, Sergey Kitaev, Seyed Ahmad Mojallal
2019 arXiv   pre-print
The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs.  ...  We will study spectral properties of the Riordan graphs in a follow up paper.  ...  This paper is dedicated to the memory of Jeff Remmel.  ... 
arXiv:1710.04604v2 fatcat:pyquociainctlicx74rcgtk2le

On the Quantization of Polygon Spaces

L. Charles
2010 Asian Journal of Mathematics  
Moduli spaces of polygons have been studied since the nineties for their topological and symplectic properties.  ...  We prove that these operators form a semiclassical integrable system, in the sense that they are Toeplitz operators with principal symbol the square of the action coordinates.  ...  The proof relies on some properties of Toeplitz operators proved in [3] that we recall now.  ... 
doi:10.4310/ajm.2010.v14.n1.a6 fatcat:sdrfnkytafcozjzwojpwlhkmqe

Page 3594 of Mathematical Reviews Vol. , Issue 86h [page]

1986 Mathematical Reviews  
This operator is said to be conjugate symmetric if there is a conjugation Q defined on the space such that the graph of X is contained in the graph of QX*Q.  ...  This criterion is applied to the Hamiltonian of three- body quantum systems interacting through long range two-body potentials.  ... 
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