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

Topological Invariance under Line Graph Transformations

Received: 6 April 2012; in revised form: 1 June 2012 / Accepted: 4 June 2012 / Published: 8 June 2012
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
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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.

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