Irregular orbital domination in graphs. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Broe, Peter; Chartrand, Gary; Zhang, Ping
• Is Part Of: International journal of computer mathematics. Volume 7:Issue 1(2022)
• Page Start: 68
• Page End: 79
• Publication Date: 2022-01-02
• Subjects: Distance -- domination -- vertex orbits -- irregular orbital sequence; 05C05 -- 05C12 -- 05C15 -- 05C69; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2021.2014977
• Languages: English
• ISSNs: 2379-9927

Abstract

Abstract : For a non-negative integer r, the r -orbit O r ( v ) of a vertex v in a connected graph G of order n is the set of vertices at distance r from v . A sequence s : r 1, r 2, …, r k of positive integers with 1 ≤ k ≤ n is called an irregular orbital dominating sequence of G if r i ≠ r j for every pair i, j of integers with 1 ≤ i < j ≤ k and G contains distinct vertices v 1, v 2, …, v k such that ⋃ i = 1 k O r i ( v i ) = V ( G ) . We investigate graphs that possess and graphs do not possess an irregular orbital dominating sequence. It is shown that a non-trivial tree has an irregular orbital dominating sequence if and only if it is neither a star, a path of order 2, nor a path of order 6.