RAINBOW VERTEX-CONNECTION NUMBER ON COMB PRODUCT OPERATION OF CYCLE GRAPH (C_4) AND COMPLETE BIPARTITE GRAPH (K_(3,N))

Rainbow vertex-connection number is the minimum colors assignment to the vertices of the graph, such that each vertex is connected by a path whose edges have distinct colors and is denoted by . The rainbow vertex connection number can be applied to graphs resulting from operations. One of the methods to create a new graph is to perform operations between two graphs. Thus, this research uses comb product operation to determine rainbow-vertex connection number resulting from comb product operation of cycle graph and complete bipartite graph  & . The research finding obtains the theorem of rainbow vertex-connection number at the graph of  for  while the theorem of rainbow vertex-connection number at the graph of  for  for

BILANGAN KETERHUBUNGAN TITIK PELANGI BEBERAPA KELAS GRAF

A graph G is called a rainbow vertex connected if every two vertices G are connected by a rainbow path, that is, a path whose all the internal vertices are of a different color. The rainbow vertex connection number of graph G denoted by rvc(G) is the minimum number of colors used to color all vertices by G such that the graph G is connected to rainbow vertex. The rainbow vertex connection number in a graph will not be less than the diameter of the graph minus one. The rainbow vertex connection number discussed in this article for various classes of graphs include complete graph Kn, complete bipartite graph Km,n  , wheel graph Wn  , two-layer wheel graph Wn2, complete multipartite graph Kn1,n2,...,nt  , path Pn, comb graph GSn, graph  , graph , graph , graph . Keywords: graph, vertex coloring, rainbow vertex connection number. &nbsp

Bilangan Terhubung Titik Pelangi Kuat Graf Octa-Chain (OCm)

An Octa-Chain graph (OCm) is a graph formed by modifying the cycle graph C8 by adding an edge connecting the midpoints in C8. The minimum number of colors used to color the vertices in a graph so that every two vertices have a rainbow path is called the rainbow vertex-connected number denoted by rvc (G). While the minimum number of colors used to color the vertices in a graph so that every two vertices are always connected by a rainbow path is called a strong rainbow vertex connected number and is denoted by srvc (G). This study aims to determine the rainbow vertex-connected number (rvc) and the strong rainbow-vertex-connected number (srvc) in the Octa-Chain graph (OCm). The results obtained from this research are the rainbow vertex-connected number rvc (OCm)=2m and the strong rainbow-vertex-connected number srvc (OCm)=2m