Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Graphs
-
Krzysztof Hryniewiecki
-
Warsaw University
-
Supported by RPBP.III-24.C1.
Summary.
-
Definitions of graphs are introduced and
their basic properties are proved.
The following notions related to graph theory are
introduced:
subgraph,
finite graph,
chain and oriented chain - as a finite sequence of edges,
path and oriented path - as a finite sequence of different edges,
cycle and oriented cycle,
incidency of graph's vertices,
a sum of two graphs,
a degree of a vertice,
a set of all subgraphs of a graph.
Many ideas of this article have been taken from [11].
MML Identifier:
GRAPH_1
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[7]
[10]
[12]
[4]
[5]
[3]
[8]
[6]
[1]
[2]
Contents (PDF format)
Bibliography
- [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
- [3]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Czeslaw Bylinski.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
- [8]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
- [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [10]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [11]
Robin Wilson.
\em Wprowadzenie do teorii grafow.
PWN, 1985.
- [12]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received December 5, 1990
[
Download a postscript version,
MML identifier index,
Mizar home page]