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.