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Using size for bounding expressions of graph invariants

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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.

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Correspondence to Pierre Hansen.

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Sedlar, J., Vukičević, D. & Hansen, P. Using size for bounding expressions of graph invariants. Ann Oper Res 188, 415–427 (2011). https://doi.org/10.1007/s10479-010-0813-z

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