Affiliation of Author(s):理学院
Journal:JOURNAL OF COMBINATORIAL OPTIMIZATION
Key Words:Eccentricity Diameter Almost self-centered graph Graph of diameter 2 ASC index
Abstract:A graph is almost self-centered (ASC) if all but two of its vertices are central. An almost self-centered graph with radius r is called an r-ASC graph. The r-ASC index of a graph G is the minimum number of vertices needed to be added to G such that an r-ASC graph is obtained that contains G as an induced subgraph. It is proved that holds for any graph G and any which improves the earlier known bound . It is further proved that holds if and G is of order at least 2. The 3-ASC index of complete graphs is determined. It is proved that if G has diameter 2 and for several classes of graphs of diameter 2 the exact value of the 3-ASC index is obtained. For instance, if a graph G of diameter 2 does not contain a diametrical triple, then . The 3-ASC index of paths of order , cycles of order , and trees of order and diameter are also determined, respectively, and several open problems proposed.
ISSN No.:1382-6905
Translation or Not:no
Date of Publication:2018-11-01
Co-author:Liu, Haiqiong,Das, Kinkar Ch,Klavzar, Sandi
Correspondence Author:Kexiang Xu