Ollivier--Ricci Idleness Functions of Graphs | Zendy

David Bourne | Zendy; D. H. Cushing | Zendy; Shiping Liu | Zendy; Florentin Münch | Zendy; Norbert Peyerimhoff | Zendy

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Ollivier--Ricci Idleness Functions of Graphs

Author(s) -

David Bourne,

D. H. Cushing,

Shiping Liu,

Florentin Münch,

Norbert Peyerimhoff

Publication year - 2018

Publication title -

siam journal on discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.843

H-Index - 66

eISSN - 1095-7146

pISSN - 0895-4801

DOI - 10.1137/17m1134469

Subject(s) - cartesian product , mathematics , piecewise linear function , combinatorics , function (biology) , graph , curvature , discrete mathematics , mathematical analysis , geometry , evolutionary biology , biology

We study the Ollivier--Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors.

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