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All Journal Desimal: Jurnal Matematika
Akadji, Afifah Farhanah
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Education Mathematics Social Sciences

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Rainbow vertex connection number and strong rainbow vertex connection number on slinky graph (SlnC4)) Akadji, Afifah Farhanah; Katili, Muhammad Rifai; Nasib, Salmun K.; Yahya, Nisky Imansyah
Desimal: Jurnal Matematika Vol. 4 No. 2 (2021): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v4i2.7276

Abstract

A graph is said rainbow connected if no path has more than one vertices of the same color inside. The minimum number of colors required to make a graph to be rainbow vertex-connected is called rainbow vertex connection-number and denoted by rvc(G) . Meanwhile, the minimum number of colors  required to make a graph to be strongly rainbow vertex-connected is called strong rainbow vertex connection-number and denoted by srvc(G). Suppose there is a simple, limited, and finite graph G. Thus, G=(V(G),E(G)) with the determination of k-coloring c:V(G)->{1,2,...,k} . The reaserch aims at determining rainbow vertex connection-number and strong rainbow vertex connection-number on slinky graphs (Sl_nC_4). Moreover, the research method applies a literature study with the following procedures; drawing slinky graphs (Sl_nC_4), looking for patterns of rainbow vertex connection-number, and strong rainbow vertex connection-number on slinky graphs (Sl_nC_4), then proving the theorems obtained from the previous pattern. It is obtained rvc(Sl_nC_4)=2n-1, srvc(Sl_2C_4)=4, and srvc(Sl_nC_4) = 3n-3 for n>= 3. 
Co-Authors NISKY IMANSYAH YAHYA Salmun K. Nasib