Local Properties of Triangular Graphs

In the paper triangular graphs are discussed. The class of triangular graphs is of special interest as unifying basic features of complete graphs with trees and being used on many various occasions. They model processor networks in which local computations can be easily implemented. The main issue addressed in the paper is to characterize class of triangular graphs (defined globally) by local means. Namely, it is proved that any triangular graph can be constructed from a singleton by successive extensions with nodes having complete neighborhoods. Next, the proved theoretical properties are applied for designing some local algorithms: for elections a leader and for constructing spanning trees of triangular graphs. The fairness of these algorithms is proved, which means that any node can be elected and any spanning tree can be obtained due to application of these algorithms.

• Type: Journal
• Year: 2007
• Where: FUIN
• Authors: Antoni W. Mazurkiewicz
• Keywords: Complete Graphs, FUIN 2007, Paper Triangular Graphs, Triangular Graphs