A new characterization of median graphs

Berrachedi, Abdelhafid

doi:10.1016/0012-365x(94)90128-7

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1999

2019

Publication Types

Select...

Article2

Other1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Berrachedi [2] characterized median graphs as the connected graphs G in which intervals I have the property that for every v ∈ V (G), there exists a unique vertex x ∈ I that attains d(v, I). As Q n is median and its subgraph H isomorphic to a k-cube is an interval of Q n , it follows that if u ∈ V (Q n ), then H contains a unique vertex that is at the minimum distance from u.…”

mentioning

confidence: 99%

Daisy cubes and distance cube polynomial

Klavžar¹,

Mollard²

2017

Preprint

View full text Add to dashboard Cite

Let X ⊆ {0, 1} n . Then the daisy cube Q n (X) is introduced as the subgraph of Q n induced by the intersection of the intervals I(x, 0 n ) over all x ∈ X. Daisy cubes are partial cubes that include Fibonacci cubes, Lucas cubes, and bipartite wheels. If u is a vertex of a graph G, then the distance cube polynomial D G,u (x, y) is introduced as the bivariate polynomial that counts the number of induced subgraphs isomorphic to Q k at a given distance from the vertex u. It is proved that if G is a daisy cube, then D G,0 n (x, y) = C G (x + y − 1), where C G (x) is the previously investigated cube polynomial of G. It is also proved that if G is a daisy cube, then D G,u (x, −x) = 1 holds for every vertex u in G.

show abstract

mentioning

confidence: 99%