Core Concepts
The author explores the broadcast independence number of oriented circulant graphs, focusing on independent broadcasts and their properties.
Abstract
The study delves into the concept of broadcast independence in oriented circulant graphs, analyzing functions and paths to determine maximum values. Various cases are considered to establish bounds and exact values for the broadcast independence number.
In-depth analysis is provided on constructing independent broadcasts with specific constraints, showcasing the intricacies of graph theory applications. The study highlights key relationships between vertices and distances in oriented circulant graphs, offering insights into optimal broadcasting strategies.
Overall, the research contributes valuable insights into the broadcast independence number of oriented circulant graphs, shedding light on fundamental concepts in graph theory analysis.
Stats
diam(−→C (2a; 1, a)) = a
βb(−→C (n; 1, a)) ≥ max{βb(G), diam(−→G)}
βb(−→C (n; 1, a)) = diam(−→C (n; 1, a)) = ⌊n/2⌋
βb(−→C (n; 1, 2)) = diam(−→C (n; 1, 2)) = ⌊n/2⌋
βb(−→C (2a - 1; 1, a)) = diam(−→C (2a - 1; 1, a)) = ⌈(2a - 1)/2⌉