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.III24.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
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