Geodesic
Trees with small spectral gap
Ars Mathematica Contemporanea, Tome 14 (2018) no. 1, pp. 197-207.

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Continuing the previous research, we consider trees with given number of vertices and minimal spectral gap. Using the computer search, we conjecture that this spectral invariant is minimized for double comet trees. The conjecture is confirmed for trees with at most 20 vertices; simultaneously no counterexamples are encountered. We provide theoretical results concerning double comets and putative trees that minimize the spectral gap. We also compare the spectral gap of regular graphs and paths. Finally, a sequence of inequalities that involve the same invariant is obtained.
DOI : 10.26493/1855-3974.992.68d
Keywords: Graph eigenvalues, double comet, extremal values, numerical computation 
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Ivana Jovović; Tamara Koledin; Zoran Stanić. Trees with small spectral gap. Ars Mathematica Contemporanea, Tome 14 (2018) no. 1, pp. 197-207. doi : 10.26493/1855-3974.992.68d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.992.68d/

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