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
Publisher: OmniScriptum, 2010

Synopsis

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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Reseņa 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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Publisher
OmniScriptum
Publication date
2010
Language
English
ISBN 10 
6130932391
ISBN 13 
9786130932398
Binding
Tapa blanda
Number of pages
72
Editor
Miller Frederic P., Vandome Agnes F., McBrewster John