Distance spectra and distance energies of iterated line graphs of regular graphs. (English) Zbl 1249.05251

Ramane, H. S.; Revankar, D. S.; Gutman, I.; Walikar, H. B.

Publ. Inst. Math., Nouv. Sér. 85(99), 39-46 (2009).

The authors show that, if an \(r\)-regular graph \(G\) with \(n\) vertices does not contain any of four small graphs as an induced subgraph, then its \(k\)-th iterated line graph \(L(L(\dots L(G)\dots))\) has exactly one positive eigenvalue of the distance matrix, equal to \(r(n-2)\), regardless of the value of \(k\).

Reviewer: Dragan Stevanović (Niš)

MSC:

05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)
05C12	Distance in graphs
05C76	Graph operations (line graphs, products, etc.)

Keywords:

distance energy; distance spectrum