Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21282220170901Graceful labelings of the generalized Petersen graphs1491591364610.22049/cco.2017.25918.1055ENAleksanderVeselUniversity of MariborZehuiShaoSchool of Information Science & Technology, Chengdu University, Chengdu, ChinaFeiDengCollege of Information Science and Technology, Chengdu University of Technology, Chengdu, ChinaZepengLiKey Laboratory of High Confidence Software Technologies, Peking University, Peking, ChinaJournal Article20170320A graceful labeling of a graph $G=(V,E)$ with $m$ edges is an injection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labels obtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersen graph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, ldots, u_n} cup {v_1, v_2, ldots, v_n}$ 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