%0 Journal Article
%T Topological Invariance under Line Graph Transformations
%A Allen D. Parks
%J Symmetry
%D 2012
%I MDPI AG
%R 10.3390/sym4020329
%X 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.
%K algebraic graph theory
%K line graph
%K Krausz decomposition
%K homology
%K graph invariant
%K Euler characteristic
%U http://www.mdpi.com/2073-8994/4/2/329