A Construction of Smooth Travel Groupoids on Finite Graphs

Diogo Kendy Matsumoto; Atsuhiko Mizusawa

doi:10.1007/s00373-015-1630-6

A Construction of Smooth Travel Groupoids on Finite Graphs

Diogo Kendy Matsumoto^*, Atsuhiko Mizusawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

A travel groupoid is an algebraic system related with graphs. In this paper, we give an algorithm to construct smooth travel groupoids for any finite graph. This algorithm gives an answer of Nebeský’s question, “Does there exist a connected graph G such that G has no smooth travel groupoid?”, in finite cases.

Original language	English
Journal	Graphs and Combinatorics
DOIs	https://doi.org/10.1007/s00373-015-1630-6
Publication status	Accepted/In press - 2015 Sept 30

Keywords

Finite graph
Smooth travel groupoid
Spanning tree
Travel groupoid

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Theoretical Computer Science

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10.1007/s00373-015-1630-6

Cite this

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title = "A Construction of Smooth Travel Groupoids on Finite Graphs",

abstract = "A travel groupoid is an algebraic system related with graphs. In this paper, we give an algorithm to construct smooth travel groupoids for any finite graph. This algorithm gives an answer of Nebesk{\'y}{\textquoteright}s question, “Does there exist a connected graph G such that G has no smooth travel groupoid?”, in finite cases.",

keywords = "Finite graph, Smooth travel groupoid, Spanning tree, Travel groupoid",

author = "Matsumoto, {Diogo Kendy} and Atsuhiko Mizusawa",

year = "2015",

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doi = "10.1007/s00373-015-1630-6",

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AU - Matsumoto, Diogo Kendy

AU - Mizusawa, Atsuhiko

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N2 - A travel groupoid is an algebraic system related with graphs. In this paper, we give an algorithm to construct smooth travel groupoids for any finite graph. This algorithm gives an answer of Nebeský’s question, “Does there exist a connected graph G such that G has no smooth travel groupoid?”, in finite cases.

AB - A travel groupoid is an algebraic system related with graphs. In this paper, we give an algorithm to construct smooth travel groupoids for any finite graph. This algorithm gives an answer of Nebeský’s question, “Does there exist a connected graph G such that G has no smooth travel groupoid?”, in finite cases.

KW - Finite graph

KW - Smooth travel groupoid

KW - Spanning tree

KW - Travel groupoid

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A Construction of Smooth Travel Groupoids on Finite Graphs

Abstract

Keywords

ASJC Scopus subject areas

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