Vol. 27, No. 2, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
On interchange graphs

Benjamin L. Schwartz

Vol. 27 (1968), No. 2, 393–396

The interchange graph I(G) for an unoriented graph G has been defined by Ore as follows: The vertices of I(G) are the edges of G; and two vertices of I(G) are connected by an edge if and only if they are adjacent (i.e., have a vertex in common) in G. In 1962 Ore raised the problem of determining those graphs for which

I(G ) = G.

This paper solves this problem for finite connected graphs with loops and parallel edges, extending earlier work on the problem.

A loop (an edge whose two ends coincide in a single vertex) is considered adjacent to itself, and hence generates another loop under the I mapping. If two edges of G connect the same two vertices, the corresponding vertices of I(G) are also connected by two distinct edges.

Mathematical Subject Classification
Primary: 05.40
Received: 26 June 1967
Published: 1 November 1968
Benjamin L. Schwartz