Paper Info
Title
-Hull Number of Graphs with Diameter Two.
Abstract
Let G be a finite, simple, undirected graph with vertex set V (G). If there is a vertex subset S ⊆ V (G), and every vertex of V (G) with at least two neighbors in S is also a member of S, then S is termed P3-convex. The P3-convex hull of of S is the smallest convex set containing S. The P3-hull number h(G) is the cardinality of a smallest set of vertices whose P3-convex hull is the entire graph. In this paper we establish some bounds on the P3-hull number of graphs with diameter two. Particularly, in biconnected C6-free diameter two graphs the P3-hull number is at most 4. We also establish the upper bound h(G)≤⌈k1+b⌉+1 or alternatively h(G)≤⌈logc+1⁡(k.c+1)⌉+1, for strongly regular graphs G(n,k,b,c).
Year
DOI
Venue
2019
10.1016/j.entcs.2019.08.028
Electronic Notes in Theoretical Computer Science
Keywords
DocType
Volume
graph,P3-convexity,hull number,diameter two
Journal
346
ISSN
Citations 
PageRank 
1571-0661
0
0.34
References 
Authors
0
6
Name
Order
Citations
PageRank
Márcia R. Cappelle132.19
Erika M. M. Coelho2155.27
Hebert Coelho302.03
Braully R. Silva400.68
Fábio Protti535746.14
Uéverton S. Souza62021.12