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020 _a9781461486992
_9978-1-4614-8699-2
024 7 _a10.1007/978-1-4614-8699-2
_2doi
050 4 _aQA166-166.247
072 7 _aPBV
_2bicssc
072 7 _aMAT013000
_2bisacsh
082 0 4 _a511.5
_223
100 1 _aPelayo, Ignacio M.
_eauthor.
245 1 0 _aGeodesic Convexity in Graphs
_h[electronic resource] /
_cby Ignacio M. Pelayo.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aVIII, 112 p. 41 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Mathematics,
_x2191-8198
520 _aGeodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most st udied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two  invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester graduate course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory.  .
650 0 _aMathematics.
650 0 _aPartial differential equations.
650 0 _aDifferential geometry.
650 0 _aGraph theory.
650 1 4 _aMathematics.
650 2 4 _aGraph Theory.
650 2 4 _aDifferential Geometry.
650 2 4 _aPartial Differential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461486985
830 0 _aSpringerBriefs in Mathematics,
_x2191-8198
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-8699-2
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c45043
_d45043