Intersection array
Encyclopedia
In the mathematical field of graph theory
, given a distance-regular graph
G of diameter
d, by definition there are integers bi and ci such that given any two vertices x and y in G at distance i, y has bi neighbours at distance i + 1 from x and ci neighbours at distance i − 1 from x. The sequence {b0, ..., bd−1;c1, ..., cd} is called the intersection array of G.
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, given a distance-regular graph
Distance-regular graph
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...
G of diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
d, by definition there are integers bi and ci such that given any two vertices x and y in G at distance i, y has bi neighbours at distance i + 1 from x and ci neighbours at distance i − 1 from x. The sequence {b0, ..., bd−1;c1, ..., cd} is called the intersection array of G.