Abstract
In a graph G=( V, E), the eccentricity e( v) of a vertex v is max { d ( v , u ) : u ∈ V } . The center of a graph is the set of vertices with minimum eccentricity. A house–hole–domino-free (HHD-free) graph is a graph which does not contain the house, the domino, and holes (cycles of length at least five) as induced subgraphs. We present an algorithm which finds a central vertex of a HHD-free graph in O( Δ 1.376| V|) time, where Δ is the maximum degree of a vertex of G. Its complexity is linear in the case of weak bipolarizable graphs, chordal graphs, and distance-hereditary graphs. The algorithm uses special metric and convexity properties of HHD-free graphs.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
