Copyright: © the author(s), publisher and licensee Technoscience Academy. This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited International Journal of Scientific Research in Science, Engineering and Technology Print ISSN: 2395-1990 | Online ISSN : 2394-4099 (www.ijsrset.com) doi : https://doi.org/10.32628/IJSRSET229436 222 The Rainbow-Vertex Connection Number [RVCN] of Subdivision of Certain Graphs Dechamma K. K. *1 , Dr. Rajanna K. R. 2 * 1 Department of Mathematics, T. John Institute of Technology, Bengaluru, Karnataka, India 2 Department of Mathematics, Acharya Institute of Technology, Bengaluru, Karnataka, India Article Info Volume 9, Issue 4 Page Number : 222-227 Publication Issue : July-August-2022 Article History Accepted : 05 July 2022 Published: 24 July 2022 ABSTRACT Rainbow-Vertex Connection Number [rvcn] is computed for some graphs by the researchers. Here we have considered the subdivision graphs of certain graph classes. The rainbow edge connection number of subdivision of Triangular snake graph was already found [1] . Using the definition of rainbow-vertex connection number [5] , which is the smallest positive integer k such that the graph is rainbow- vertex connected, we find the rainbow vertex number of subdivision graph of Friendship graph ((  )) =  + 2 ∀  ≥2 ,, Triangular snake graph ((  )) = 2 − 1 ∀ ≥3 and Comb graph ((  ʘ 1 )) = 3 − 1 ∀ ≥ 2 . Keywords: Rainbow Vertex Connected Graph and Number, Friendship Graph, Triangular Graph, Comb Graph, Subdivision Graph. I. INTRODUCTION We consider simple, finite, connected, and undirected subdivision graphs. A graph is a set of vertices and edges (  ,  ) ,   ′ are non-empty. Krivelevich and Yuster [5] introduced the rainbow-vertex connection number, and Li and Shi investigated it. The lower bound was stated by Krivelevich and Yuster as () ≥ () − 1 . Definition 1.1: Graph Colouring: Proper colouring is the process of colouring each vertex of a graph so that no two neighbouring vertices have the same colour. Definition 1.2: Rainbow colouring: A path in an edge- coloured graph is claimed to be rainbow coloured if no colour repeats thereon path. Definition 1.3: Rainbow vertex connected graph: If all of a graph's internal vertices have unique colours, the graph is said to have a rainbow vertex path. If there is a path connecting every pair of vertices in the network or graph, it is said to be rainbow vertex connected. Definition 1.4: Friendship graph: It is a planar graph with 2 + 1 vertices and 3 edges. This graph is constructed by joining n-copies of the cycle graph  3 with a common vertex, which is called as universal vertex for the graph. It is also called as Dutch windmill or  -fan graph.