On interchange graphs

  title={On interchange graphs},
  author={B. L. Schwartz},
  journal={Pacific Journal of Mathematics},
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 / mapping. If two edges of G connect the same two vertices, the corresponding vertices of I(G) are also connected by two distinct edges. 

Figures from this paper

Locally finite self-interchange graphs
Graphs isomorphic to their interchanges are studied. Using prior results of more special cases, plus one new concept, it is possible to characterize all locally finite self-interchange graphs, finiteExpand
Fundamental groups of iterated line graphs
The rank of the fundamental group, , of a connected graph is related to the Euler characteristic, , of by in this article, the Euler characteristic of the iterated line graph of and its complement isExpand
The dynamics of the line and path graph operators
This paper states that for any integerk e 1 thek- path graph Pk(G) of a graph G has all length-k subpaths ofG as vertices, and two such vertices are adjacent whenever their union forms a path or cycle withk + 1 edges. Expand
A bibliography of graph equations
A classification and a large bibliography of graph equations are offered, in which the unknowns are graphs and many problems and results in graph theory can be formulated in terms of graphs. Expand


The interchange graph of a finite graph
Let G be a finite graph. The interchange graph G' of G, has a vertex corresponding to each edge of G, two vertices of G' being connected if the corresponding edges of G have a common vertex in G. InExpand
Theory of Graphs
Fundamental concepts Connectedness Path problems Trees Leaves and lobes The axiom of choice Matching theorems Directed graphs Acyclic graphs Partial order Binary relations and Galois correspondencesExpand
The theory of graphs and its applications
This book on the theory of graphs provides the reader with a mathematical tool which can be used in the behavioral sciences, in the theory of information, cybernetics, games, transport networks, asExpand
Osservazioni sulle caratteristiche dei grafi o singrammi
RiassuntoSi introducono certi gruppi di numeri associati ad un grafo o singrammaG che vengono chiamati caratteristiche diG. Si studiano alcune proprietà delle caratteristiche e se ne fannoExpand
The isomorphism between graphs and their adjoint graphs
grafo commutato e sul grafσ opposoto di un grafo orientato
  • Atti, Sem. Mat. Fis. Univ. Modena
  • 1965
USMC, private communication with the author
  • 1964