arXiv:1204.2981 Abstract | arXiv Analytics

arXiv:1204.2981 [math.CO]Abstract References Reviews Resources

A connection between the bipartite complements of line graphs and the line graphs with two positive eigenvalues

Published 2012-04-13Version 1

In 1974 Cvetkovi\'c and Simi\'c showed which graphs $G$ are the bipartite complements of line graphs. In 2002 Borovi\'canin showed which line graphs $L(H)$ have third largest eigenvalue $\lambda_3\leq0$. Our first observation is that two of the graphs Borovi\'canin found are the complements of two of the graphs found by Cvetkovi\'c and Simi\'c. Using the Courant-Weyl inequalities we show why this is and reprove the result of Borovi\'canin, highlighting some features of the graphs found by both.

Comments: 4 pages, 2 figures

Categories: math.CO

Subjects: 05C50

Keywords: line graphs, bipartite complements, positive eigenvalues, connection, third largest eigenvalue

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