Some star complements for the second largest eigenvalue of a graph

Zoran Stanić

Abstract


The star complement technique is a spectral tool recently developed for constructing some bigger graphs from their smaller parts, called star complements. The most frequently, the implementation of those technique requires using the computers. Therefrom, we develop an SCL (star complement library) – the set of programs providing easy and quick implementation of those technique. Here, we present the facilities of SCL. In further, we determine some star complements for 1 or (√5 – 1)/2 as the second largest eigenvalue of a graph. Finally, using the SCL, we consider the maximal extensions of the star complements obtained.

Keywords


Adjacency matrix, graph eigenvalues, star complement, divisor concept, mathematical software

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DOI: https://doi.org/10.26493/1855-3974.11.d83

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications