Interdisciplinary Information Sciences

On the Triviality of Bouquets and Tunnel Number One Links

Toshio HARIKAE

Article type: Others
Subject area: Others
2001 Volume 7 Issue 1 Pages 1-3
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.1

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In this paper, we discuss the triviality of bouquets by using the tangle description, and give a necessary and sufficient condition for a bouquet to be trivial. We also give a necessary and sufficient condition for a tunnel number one knot to be a 2-bridge knot and prove that if each component of a tunnel number one link is a trivial knot, then the link is 2-bridge.

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A Condition for a Graph in the Disc to Contain the Half Hemisphere of the Dodecahedron —Application to Dehn Surgery Theory—

Chuichiro HAYASHI, Koya SHIMOKAWA

2001 Volume 7 Issue 1 Pages 5-16
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.5

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Half Plane Models for Divides, Their Knots and Dowker-Thistlethwaite Codes

Masaharu ISHIKAWA

2001 Volume 7 Issue 1 Pages 17-24
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.17

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The divide is a new and interesting object which was introduced by N. A'Campo as an extension of complex plane curve singularities. In this paper we construct regular knot diagrams of the knots of divides by using half plane models and present a systematic algorithm for making Dowker-Thistlethwaite codes of the knots from the divides.

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A Survey on Hamiltonian Cycles

Ken-ichi KAWARABAYASHI

2001 Volume 7 Issue 1 Pages 25-39
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.25

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In this article, we give a survey hamiltonian theorems, problems and conjectures in graph theorical aspect which supplements a well-known survey of Gould.

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Distributions on Graphs and Walks

Akinori MATSUI

2001 Volume 7 Issue 1 Pages 41-43
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.41

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Variations of Graphs in Riemannian Manifolds

Akinori MATSUI

2001 Volume 7 Issue 1 Pages 45-51
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.45

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Zeta Functions for Images of Graph Coverings by Some Operations

Hirobumi MIZUNO, Iwao SATO

2001 Volume 7 Issue 1 Pages 53-60
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.53

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We consider the zeta functions of the line graph and the middle graph of a regular covering of a graph G, and their related topics. Let M (G) be the middle graph of G and T (G) the total graph of G. We show that the middle graph and the total graph of a regular covering of a graph G with covering transformation group A is a regular covering of M (G) and T (G) with the same covering transformation group A, respectively. For a regular graph G, we express the zeta functions of the line graph and the middle graph of a regular covering of G by using the characteristic polynomial of that regular covering.

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A Criterion for a Graph to Admit a Tight Substantial Map into the Euclidean n-space

Hirofumi NAGASAKA

2001 Volume 7 Issue 1 Pages 61-66
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.61

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We give a sufficient and necessary condition for a finite graph to admit a tight and substantial polygonal map into the n-dimensional Euclidean space. As a consequence, we determine the curvature dimension for 2-connected graphs explicitly from their topological structure.

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Spectra of Arithmetic Infinite Graphs and Their Application

Hirofumi NAGOSHI

2001 Volume 7 Issue 1 Pages 67-76
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.67

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We discuss some properties of certain finite volume infinite graphs defined arithmetically, from a spectral point of view. These graphs are constructed from principal congruence subgroups over function fields and known to be Ramanujan diagrams.

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Quadrangulations on Closed Surfaces

Atsuhiro NAKAMOTO

2001 Volume 7 Issue 1 Pages 77-98
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.77

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In this paper, we give a survey of results on quadrangulations on closed surfaces, especially on diagonal transformations and related topics.

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Topological Graph Theory from Japan

Seiya NEGAMI

2001 Volume 7 Issue 1 Pages 99-112
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.99

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This is a survey of studies on topological graph theory developed by Japanese people in the recent two decades and presents a big bibliography including almost all papers written by Japanese topological graph theorists.

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Clasp-pass Moves on Spatial Graphs

Ryo NIKKUNI

2001 Volume 7 Issue 1 Pages 113-121
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.113

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In this paper our main object is the graph embedded into the 3-space, called the spatial graph. We study a clasp-pass equivalence on spatial graphs, which is an equivalence relation generated by clasp-pass moves and ambient isotopies. Our approach is an analogy of the delta equivalence classification on spatial graphs, where a delta equivalence is an equivalence relation generated by delta moves and ambient isotopies and implied by a clasp-pass equivalence. Consequently, clasp-pass classifications on spatial embeddings of several non-planar graphs and a specified planar graph are given. This is a preliminary report on our recent work and details will appear elsewhere.

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Algorithmic Aspects of Pyramidal Tours with Restricted Jump-Backs

Yoshiaki ODA, Katsuhiro OTA

2001 Volume 7 Issue 1 Pages 123-133
Published: 2001
Released on J-STAGE: June 11, 2003

DOIhttps://doi.org/10.4036/iis.2001.123

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This paper discusses several classes of restricted traveling salesman tours and polynomial time algorithms to find a shortest tour in those classes. Here we consider the constraints for intervals of edges in a tour. Each restricted tour is an extension of a pyramidal tour and the algorithms can be applied for special cases of the traveling salesman problem.

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