Cycles and components in geometric graphs: adjacency operator approachReport as inadecuate




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1 IECN - Institut Élie Cartan de Nancy 2 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications 3 Department of Mathematics and Statistics - Southern Illinois University

Abstract : Nilpotent and idempotent adjacency operator methods are applied to the study of random geometric graphs in a discretized, $d$-dimensional unit cube$0; 1$^d. Cycles are enumerated, sizes of maximal connected compo- nents are computed, and closed formulas are obtained for graph circumfer- ence and girth. Expected numbers of $k$-cycles, expected sizes of maximal components, and expected circumference and girth are also computed by considering powers of adjacency operators.





Author: René Schott - Stacey Staples -

Source: https://hal.archives-ouvertes.fr/



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