# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

E. Cheng, L.-H. Hsu, C.-N. Hung, M.-C. Yang

Title:

2-spanning cyclability problems of the some generalized Petersen graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2017-09-18, Revised: 2018-03-05, Accepted: 2018-03-05, https://doi.org/10.7151/dmgt.2150

Abstract:

A graph $G$ is called $r$-spanning cyclable if for every $r$ distinct vertices $v_1,v_2,\ldots,v_r$ of $G$, there exists $r$ cycles $C_1,C_2,\ldots, C_r$ in $G$ such that $v_i$ is on $C_i$ for every $i$, and every vertex of $G$ is on exactly one cycle $C_i$. In this paper, we consider the $2$-spanning cyclable problem for the generalized Petersen graph $GP(n,k)$. We solved the problem for $k\leq 4$. In addition, we provide an additional observation for general $k$ as well as stating a conjecture.

Keywords:

Petersen graph, spanning cyclable