Geodetic Variants of Sierpinski Triangles - Mathew, Deepa; Xavier, D. Antony (International Journal of Computer Sciences and Engineering, 2025)
The concept of convex sets in the classical Euclidean geometry was extended to graphs and different graph convexities were studied based on the kind of path that is considered. The geodetic number of a graph is one of the extensively studied graph theoretic parameters concerning geodesic convexity in graphs. A u-v geodesic is a u-v path of length d(u,v) in G. For a non-trivial connected graph G , a set S ⊆ V (G) is called a geodetic set if every vertex not in S lies on a geodesic between two vertices from S. The cardinality of the minimum geodetic set of G is the geodetic number g(G) of G. The Sierpinski triangle , also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. In this paper some of the geodetic variants including hull number, monophonic hull number, geodetic number, strong geodetic number , total geodetic number ,upper geodetic number, open geodetic number and strong open geodetic number for Sierpinski triangle is investigated.