Scrambling Index dari Graf Ring-Star dan Variasinya

Abstract

A connected graph G is called primitive provided that there is a positive integer k such that for each pair of vertices u dan v in G there is a walk of length k connecting u and v. A scrambling index of a primitive graph G, k(G), is the smallest positive integer k such that for each pair of distinct vertices u and v there is a vertex w with the property that there is a walk connecting u and v and a walk connecting v and w of length k. For a s-ring star R with cycle of odd length s we show that k(R) = (s + 1)/2. Two others variation of ring star graph is s-wheel (W) graphand s-steering ship (S), we show that k(W) = 1 for s-wheel graph and k(S) = 2 for s-steering ship graph.