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On the forcing spectrum of generalized Petersen graphs P(n,2)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zhao, Shuang Zhu, Jinjiang Zhang, Heping |
| Copyright Year | 2017 |
| Abstract | The forcing number of a perfect matching $M$ of a graph $G$ is the smallest cardinality of subsets of $M$ that are contained in no other perfect matchings of $G$. The forcing spectrum of $G$ is the collection of forcing numbers of all perfect matchings of $G$. In this paper, we classify the perfect matchings of a generalized Petersen graph $P(n,2)$ in two types, and show that the forcing spectrum is the union of two integer intervals. For $n\ge 34$, it is $\left[\lceil \frac { n }{ 12 } \rceil+1,\lceil \frac { n+3 }{ 7 } \rceil +\delta (n)\right]\cup \left[\lceil \frac { n+2 }{ 6 } \rceil,\lceil \frac { n }{ 4 } \rceil\right]$, where $\delta (n)=1$ if $n\equiv 3$ (mod 7), and $\delta (n)=0$ otherwise. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://export.arxiv.org/pdf/1707.03701 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1707.03701v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
