Distance-Regular Graph: Mathematics, Regular graph, Graph (mathematics), Distance (graph theory), Distance-transitive graph, Graph automorphism, Strongly regular graph - Softcover

 
9786130932398: Distance-Regular Graph: Mathematics, Regular graph, Graph (mathematics), Distance (graph theory), Distance-transitive graph, Graph automorphism, Strongly regular graph
Softcover
ISBN 10: 6130932391 ISBN 13: 9786130932398
Verlag: OmniScriptum, 2010

Inhaltsangabe

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w at distance i the number of vertices adjacent to w and at distance j from v is the same. Every distance-transitive graph is distance regular. Indeed, distance-regular graphs were introduced as a combinatorial generalization of distance-transitive graphs, having the numerical regularity properties of the latter without necessarily having a large automorphism group. Alternatively, a distance-regular graph is a graph for which there exist integers bi,ci,i=0,...,d such that for any two vertices x,y in G and distance i=d(x,y), there are exactly ci neighbors of y in Gi-1(x) and bi neighbors of y in Gi+1(x), where Gi(x) is the set of vertices y of G with d(x,y)=i (Brouwer et al. 1989, p. 434). The array of integers characterizing a distance-regular graph is known as its intersection array. A distance-regular graph with diameter 2 is strongly regular, and conversely (unless the graph is disconnected).

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w at distance i the number of vertices adjacent to w and at distance j from v is the same. Every distance-transitive graph is distance regular. Indeed, distance-regular graphs were introduced as a combinatorial generalization of distance-transitive graphs, having the numerical regularity properties of the latter without necessarily having a large automorphism group. Alternatively, a distance-regular graph is a graph for which there exist integers bi,ci,i=0,...,d such that for any two vertices x,y in G and distance i=d(x,y), there are exactly ci neighbors of y in Gi-1(x) and bi neighbors of y in Gi+1(x), where Gi(x) is the set of vertices y of G with d(x,y)=i (Brouwer et al. 1989, p. 434). The array of integers characterizing a distance-regular graph is known as its intersection array. A distance-regular graph with diameter 2 is strongly regular, and conversely (unless the graph is disconnected).

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Verlag
OmniScriptum
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
6130932391
ISBN 13 
9786130932398
Einband
Tapa blanda
Anzahl der Seiten
72
Herausgeber
Miller Frederic P., Vandome Agnes F., McBrewster John
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar