Directed and Undirected Graphs

Guerino Mazzola; Maria Mannone; Yan Pang

doi:10.1007/978-3-319-42937-3_15

Directed and Undirected Graphs

Guerino Mazzola, Maria Mannone, Yan Pang

Music (Twin Cities)

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Up to now, we have been able to construct all basic number domains ℕ, ℤ, ℚ, ℝ, ℂ. But we have not considered geometric objects. This chapter begins to fill that gap. It introduces the most elementary geometric objects: graphs—systems of points and arrows connected by directed or undirected lines. We shall conclude part IV with the introduction of higher-dimension graphical objects that relate to coverings of sets by a system of subsets.

Original language	English (US)
Title of host publication	Computational Music Science
Publisher	Springer Nature
Pages	121-127
Number of pages	7
DOIs	https://doi.org/10.1007/978-3-319-42937-3_15
State	Published - 2016

Publication series

Name	Computational Music Science
ISSN (Print)	1868-0305
ISSN (Electronic)	1868-0313

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

Category Theory
Hamilton Cycle
Span Tree
Undirected Graph
Unordered Pair

Publisher link

10.1007/978-3-319-42937-3_15

Find It

Find It at U of M Libraries

Cite this

@inbook{87397014f98f40dc8fefc7970f37b2c1,

title = "Directed and Undirected Graphs",

abstract = "Up to now, we have been able to construct all basic number domains ℕ, ℤ, ℚ, ℝ, ℂ. But we have not considered geometric objects. This chapter begins to fill that gap. It introduces the most elementary geometric objects: graphs—systems of points and arrows connected by directed or undirected lines. We shall conclude part IV with the introduction of higher-dimension graphical objects that relate to coverings of sets by a system of subsets.",

keywords = "Category Theory, Hamilton Cycle, Span Tree, Undirected Graph, Unordered Pair",

author = "Guerino Mazzola and Maria Mannone and Yan Pang",

note = "Publisher Copyright: {\textcopyright} 2016, Springer International Publishing Switzerland.",

year = "2016",

doi = "10.1007/978-3-319-42937-3_15",

language = "English (US)",

series = "Computational Music Science",

publisher = "Springer Nature",

pages = "121--127",

booktitle = "Computational Music Science",

address = "United States",

}

TY - CHAP

T1 - Directed and Undirected Graphs

AU - Mazzola, Guerino

AU - Mannone, Maria

AU - Pang, Yan

PY - 2016

Y1 - 2016

N2 - Up to now, we have been able to construct all basic number domains ℕ, ℤ, ℚ, ℝ, ℂ. But we have not considered geometric objects. This chapter begins to fill that gap. It introduces the most elementary geometric objects: graphs—systems of points and arrows connected by directed or undirected lines. We shall conclude part IV with the introduction of higher-dimension graphical objects that relate to coverings of sets by a system of subsets.

AB - Up to now, we have been able to construct all basic number domains ℕ, ℤ, ℚ, ℝ, ℂ. But we have not considered geometric objects. This chapter begins to fill that gap. It introduces the most elementary geometric objects: graphs—systems of points and arrows connected by directed or undirected lines. We shall conclude part IV with the introduction of higher-dimension graphical objects that relate to coverings of sets by a system of subsets.

KW - Category Theory

KW - Hamilton Cycle

KW - Span Tree

KW - Undirected Graph

KW - Unordered Pair

UR - http://www.scopus.com/inward/record.url?scp=85136715353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85136715353&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42937-3_15

DO - 10.1007/978-3-319-42937-3_15

M3 - Chapter

AN - SCOPUS:85136715353

T3 - Computational Music Science

SP - 121

EP - 127

BT - Computational Music Science

PB - Springer Nature

ER -

Directed and Undirected Graphs

Abstract

Publication series

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this