On Simply Structured Kernel Bases of Unicyclic Graphs

Abstract

In this paper all those unicyclic graphs are characterized for which there exists a basis of the kernel that consists only of vectors with entries from {-1, 0, 1}. Three different characterizations are obtained, based on an algorithmic, an algebraic, and a structural criteria, respectively. Algorithmic construction of such bases is discussed as well.

Keywords:

• unicyclic
• kernel
• null space
• basis
• Gaussian elimination

2000 Mathematics Subject Classification:

• Primary 05C50
• Secondary 15A18