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.
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
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.
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.
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
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.
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
is an equivalence relation generated by delta moves
and ambient isotopies and implied by a clasp-pass
equivalence. Consequently, clasp-pass classifications on
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.
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.