Total Rainbow Connection Number Of Shackle Product Of Antiprism Graph (〖AP〗_3)

Function if  is said to be k total rainbows in , for each pair of vertex  there is a path called  with each edge and each vertex on the path will have a different color. The total connection number is denoted by trc  defined as the minimum number of colors needed to make graph  to be total rainbow connected. Total rainbow connection numbers can also be applied to graphs that are the result of operations. The denoted shackle graph  is a graph resulting from the denoted graph  where t is number of copies of G. This research discusses rainbow connection numbers rc and total rainbow connection trc(G) using the shackle operation, where  is the antiprism graph . Based on this research, rainbow connection numbers rc shack , and total rainbow connection trc shack for .Fungsi jika c : G → {1,2,. . . , k} dikatakan k total pelangi pada G, untuk setiap pasang titik  terdapat lintasan disebut x-y dengan setiap sisi dan setiap titik pada lintasan akan memiliki warna berbeda. Bilangan terhubung total pelangi dilambangkan dengan trc(G), didefinisikan sebagai jumlah minimum warna yang diperlukan untuk membuat graf G menjadi terhubung-total pelangi. Bilangan terhubung total pelangi juga dapat diterapkan pada graf yang merupakan hasil operasi. Graf shackle yang dilambangkan (G1,G2,…,Gt) adalah graf yang dihasilkan dari graf G yang dilambangkan (G,t) dengan t adalah jumlah salinan dari  Penelitian ini membahas mengenai bilangan terhubung pelangi rc dan bilangan terhubung total pelangi trc(G)menggunakan operasi shackle, dimana G adalah graf Antiprisma (AP3)Berdasarkan penelitian ini, diperoleh bilangan terhubung pelangi rc(shack AP3,t )= t+2, dan total pelangi trc(shack AP3,t)=2t+3 untuk t ≥2

An updated survey on rainbow connections of graphs - a dynamic survey

The concept of rainbow connection was introduced by Chartrand, Johns, McKeon and Zhang in 2008. Nowadays it has become a new and active subject in graph theory. There is a book on this topic by Li and Sun in 2012, and a survey paper by Li, Shi and Sun in 2013. More and more researchers are working in this field, and many new papers have been published in journals. In this survey we attempt to bring together most of the new results and papers that deal with this topic. We begin with an introduction, and then try to organize the work into the following categories, rainbow connection coloring of edge-version, rainbow connection coloring of vertex-version, rainbow $k$-connectivity, rainbow index, rainbow connection coloring of total-version, rainbow connection on digraphs, rainbow connection on hypergraphs. This survey also contains some conjectures, open problems and questions for further study

Pelabelan Prima pada Graf Simpul Semi Total dari Graf Sikat

Artikel ini membahas mengenai pelabelan prima pada suatu graf sederhana  dengan himpunan simpul  dan himpunan sisi . Suatu graf  adalah graf prima jika terdapat pemetaan bijektif  sedemikian sehingga untuk setiap simpul  dan  yang bertetangga berlaku FPB. Selanjutnya, untuk graf sederhana yang berupa graf simpul semi total dari graf sikat, dikonstruksi suatu pelabelan prima dengan pembuktiannya memanfaatkan algoritma Euclidean. Hasil konstruksi menunjukkan bahwa graf simpul semi total dari graf sikat merupakan graf prima.Kata Kunci: Pemetaan; Graf Prima; Relatif Prima; Faktor Persekutuan Terbesar Prime Labeling for a Semi-Total Point Graph of a Brush GraphABSTRACTIn this article, we investigate prime labeling for a simple graph G, where V(G) and E(G) are vertex set and edge set of G, respectively. A graph G is called a prime graph if there exists a bijective mapping  such that for each u and v are adjacent vertices in G then we have GCD. Furthermore, in terms of a semi-total point graph of a brush graph, a prime labeling was constructed using the Euclidean algorithm. As a result, this graph was a prime graph