Using size for bounding expressions of graph invariants

Jelena Sedlar (), Damir Vukičević () and Pierre Hansen ()

Annals of Operations Research, 2011, vol. 188, issue 1, 415-427

Abstract: With the help of the AutoGraphiX system, we study relations of the form $$\underline{b}_m \le i_1(G) \oplus i_2(G) \le\overline{b}_m$$ where i 1 (G) and i 2 (G) are invariants of the graph G, ⊕ is one of the operations −,+,/,×, $\underline{b}_{m}$ and $\overline{b}_{m}$ are best possible lower and upper bounding functions depending only one the size m of G. Specifically, we consider pairs of indices where i 1 (G) is a measure of distance, i.e., diameter, radius or average eccentricity, and i 2 (G) is a measure of connectivity, i.e., minimum degree, edge connectivity and vertex connectivity. Conjectures are obtained and then proved in almost all cases. Copyright Springer Science+Business Media, LLC 2011

Keywords: Size; Connectivity; Distance; Extremal graph; AGX (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10479-010-0813-z

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