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Hamiltonian properties of Toeplitz graphs

1996
*
Discrete Mathematics
*

Conditions are given for the existence

doi:10.1016/0012-365x(95)00111-9
fatcat:q44s2y5vmfegldljt7atmj7joe
*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. ...##
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The Property of Hamiltonian Connectedness in Toeplitz Graphs

2020
*
Complexity
*

A

doi:10.1155/2020/5608720
fatcat:nkgd6f3xararvlsbyi4u2t5xzi
*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. ...##
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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]

2014
*
Springer Proceedings in Mathematics & Statistics
*

The

doi:10.1007/978-3-0348-0859-0_8
fatcat:itesg2et7fbd5mbn4bojdygayq
*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. ...##
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On hamiltonian Toeplitz graphs

2002
*
Discrete Mathematics
*

We consider

doi:10.1016/s0012-365x(01)00136-4
fatcat:f3iy4ondubae7cvc5w2uikudbe
*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. ...##
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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.” ...##
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Counting independent sets in Riordan graphs
[article]

2020
*
arXiv
*
pre-print

The notion

arXiv:2006.16579v1
fatcat:fgzf5wrvaza33huoshr6x5fjs4
*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). ...##
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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,}. ...##
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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. ...##
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Characterizing bipartite Toeplitz graphs

2001
*
Theoretical Computer Science
*

A

doi:10.1016/s0304-3975(00)00230-9
fatcat:6njt6dsvcjfn3lwsl3gnk6c4ne
*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] . ...##
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Toeplitz algebras and spectral results for the one-dimensional Heisenberg model

2006
*
Journal of Mathematical Physics
*

This class contains the

doi:10.1063/1.2222083
fatcat:zsdzrvetlzgjngegmvqckvuakm
*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. ...##
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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 ...##
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Riordan graphs I: Structural properties
[article]

2019
*
arXiv
*
pre-print

The Riordan

arXiv:1710.04604v2
fatcat:pyquociainctlicx74rcgtk2le
*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. ...##
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On the Quantization of Polygon Spaces

2010
*
Asian Journal of Mathematics
*

Moduli spaces

doi:10.4310/ajm.2010.v14.n1.a6
fatcat:sdrfnkytafcozjzwojpwlhkmqe
*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. ...##
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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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