Abstract
In this paper we introduce a design, called “geodetic-design" arising from geodetic sets in a graph. A geodetic-design, over a regular graph is an ordered pair D = (V, B), where V = V (G) and B, the set of all geodetic sets, called blocks, containing vertices belonging to geodetic sets, such that every pair of non-adjacent vertices appears in exactly µ blocks. We first find governing results of a geodetic-design, if it exists, and then get such PBIB-designs for different products of graphs. It is common to have geodetic sets of graphs to be independent sets, hence we extend the designs obtained from maximum independent sets of graphs to geodetic-designs for products of graphs.
Recommended Citation
Huilgol, Medha Itagi and M.D, Vidya
(2024).
(R2096) PBIB-Designs Associated with Products of Graphs,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 20,
Iss.
1, Article 21.
Available at:
https://digitalcommons.pvamu.edu/aam/vol20/iss1/21