Back to Search
Start Over
Maximum Frustration in Signed Generalized Petersen Graphs
- Source :
- Indian journal of discrete mathematics, vol 5, no. 2 (2019) , 77-93
- Publication Year :
- 2019
-
Abstract
- A \textit{signed graph} is a simple graph whose edges are labelled with positive or negative signs. A cycle is \textit{positive} if the product of its edge signs is positive. A signed graph is \textit{balanced} if every cycle in the graph is positive. The \textit{frustration index} of a signed graph is the minimum number of edges whose deletion makes the graph balanced. The \textit{maximum frustration} of a graph is the maximum frustration index over all sign labellings. In this paper, first, we prove that the maximum frustration of generalized Petersen graphs $P_{n,k}$ is bounded above by $\left\lfloor \frac{n}{2} \right\rfloor + 1$ for $\gcd(n,k)=1$, and this bound is achieved for $k=1,2,3$. Second, we prove that the maximum frustration of $P_{n,k}$ is bounded above by $d\left\lfloor \frac{n}{2d} \right\rfloor + d + 1$, where $\gcd(n,k)=d\geq2$.
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Journal :
- Indian journal of discrete mathematics, vol 5, no. 2 (2019) , 77-93
- Publication Type :
- Report
- Accession number :
- edsarx.1905.05548
- Document Type :
- Working Paper