Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21282220170901Graceful labelings of the generalized Petersen graphs1491591364610.22049/cco.2017.25918.1055ENAleksander VeselUniversity of MariborZehui ShaoSchool of Information Science & Technology, Chengdu University, Chengdu, ChinaFei DengCollege of Information Science and Technology, Chengdu University of Technology, Chengdu, ChinaZepeng LiKey Laboratory of High Confidence Software Technologies, Peking University, Peking, China20170320 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set is ${u_iu_{i+1}, u_iv_i, v_iv_{i+k} : 1 leq i leq n }$, where subscript arithmetic is done modulo $n$. We propose a backtracking algorithm with a specific static variable ordering and dynamic value ordering to find graceful labelings for generalized Petersen graphs.Experimental results show that the presented approach strongly outperforms the standard backtracking algorithm. The proposed algorithm is able to find graceful labelings for all generalized Petersen graphs $P(n, k)$ with $n le 75$ within only several seconds.]]>http://comb-opt.azaruniv.ac.ir/article_13646_07d33d001066dc9b0e695120e6125c8a.pdf