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- Title
BALANCED UNITARY CAYLEY SIGRAPHS OVER FINITE COMMUTATIVE RINGS.
- Authors
MEEMARK, YOTSANAN; SUNTORNPOCH, BORWORN
- Abstract
Let R be a finite commutative ring with identity 1. The unitary Cayley graph of R, denoted by GR, is the graph whose vertex set is R and the edge set {{a, b} : a, b ∈ R and a - b ∈ R×}, where R× is the group of units of R. We define the unitary Cayley signed graph (or unitary Cayley sigraph in short) to be an ordered pair 풮R = (GR, σ), where GR is the unitary Cayley graph over R with signature σ : E(GR) → {1, -1} given by In this paper, we give a criterion on R for SR to be balanced (every cycle in 풮R is positive) and a criterion for its line graph L(풮R) to be balanced. We characterize all finite commutative rings with the property that the marked sigraph 풮R,μ is canonically consistent. Moreover, we give a characterization of all finite commutative rings where 풮R, η(풮R) and L(풮R) are hyperenergetic balanced.
- Subjects
UNITARY groups; COMMUTATIVE rings; RING theory; CAYLEY graphs; GRAPH theory; FINITE rings
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 5, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498813501521