Symmetry 2012, 4(2), 329-335; doi:10.3390/sym4020329
Article

Topological Invariance under Line Graph Transformations

Electromagnetic and Sensor Systems Department, Naval Surface Warfare Center Dahlgren Division, 18444 Frontage Road Suite 327, Dahlgren, VA 22448-5161, USA
Received: 6 April 2012; in revised form: 1 June 2012 / Accepted: 4 June 2012 / Published: 8 June 2012
PDF Full-text Download PDF Full-Text [177 KB, uploaded 8 June 2012 14:02 CEST]
Abstract: It is shown that the line graph transformation G L(G) of a graph G preserves an isomorphic copy of G as the nerve of a finite simplicial complex K which is naturally associated with the Krausz decomposition of L(G). As a consequence, the homology of K is isomorphic to that of G. This homology invariance algebraically confirms several well known graph theoretic properties of line graphs and formally establishes the Euler characteristic of G as a line graph transformation invariant.
Keywords: algebraic graph theory; line graph; Krausz decomposition; homology; graph invariant; Euler characteristic

Article Statistics

Load and display the download statistics.

Citations to this Article

Cite This Article

MDPI and ACS Style

Parks, A.D. Topological Invariance under Line Graph Transformations. Symmetry 2012, 4, 329-335.

AMA Style

Parks AD. Topological Invariance under Line Graph Transformations. Symmetry. 2012; 4(2):329-335.

Chicago/Turabian Style

Parks, Allen D. 2012. "Topological Invariance under Line Graph Transformations." Symmetry 4, no. 2: 329-335.

Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert