Exponent and scrambling index of double alternate circular snake graphs

4th International Conference on Operational Research

Rahmayanti, Sri^1 ; Pasaribu, Valdo E.^1 ; Nasution, Sawaluddin^1 ; Liani Salnaz, Sishi^1

Department of Mathematics, University of Sumatera Utara, Medan

20155, Indonesia^1

关键词: Graph G;    Odd length;    Positive integers;    Scrambling indices;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/300/1/012079/pdf
DOI  :  10.1088/1757-899X/300/1/012079

来源: IOP

【 摘 要 】

A graph is primitive if it contains a cycle of odd length. The exponent of a primitive graph G, denoted by exp(G), is the smallest positive integer k such that for each pair of vertices u and v in G there is a uv-walk length k. The scrambling index of a primitive graph G, denoted by k(G), is the smallest positive integer k such that for each pair of vertices u and v in G there is a uv-walk of length 2k. For an even positive integer n and an odd positive integer r, a (n,r)-double alternate circular snake graph, denoted by DA(Cr,n), is a graph obtained from a path u1u2 unby replacing each edge of the form u2iu2i+1by two different r-cycles. We study the exponent and scrambling index of DA(Cr,n) and show that exp(DA(Cr,n)) = n + r - 4 and k(DA(Cr,n)) = (n + r - 3)/2.