Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be \textit{analogous} if the larger stable sets, in both caterpillars, have the same cardinality. We study the conditions that allow us to replace, within a gracefully labeled graph, some snakes (or paths) by analogous caterpillars, to produce a new graceful graph. We present five families of graphs where this replacement is feasible, generalizing in this way some existing results: subdivided trees, first attachment trees, path-like trees, two-point union of paths, and armed crowns.
Barrientos,C and Minion,S M. (2018). Snakes and Caterpillars in Graceful Graphs. Journal of Algorithms and Computation, 50(issue 2), 37-47. doi: 10.22059/jac.2018.69503
MLA
Barrientos,C , and Minion,S M. "Snakes and Caterpillars in Graceful Graphs", Journal of Algorithms and Computation, 50, issue 2, 2018, 37-47. doi: 10.22059/jac.2018.69503
HARVARD
Barrientos C, Minion S M. (2018). 'Snakes and Caterpillars in Graceful Graphs', Journal of Algorithms and Computation, 50(issue 2), pp. 37-47. doi: 10.22059/jac.2018.69503
CHICAGO
C Barrientos and S M Minion, "Snakes and Caterpillars in Graceful Graphs," Journal of Algorithms and Computation, 50 issue 2 (2018): 37-47, doi: 10.22059/jac.2018.69503
VANCOUVER
Barrientos C, Minion S M. Snakes and Caterpillars in Graceful Graphs. J. Algo. Comp.. 2018;50(issue 2):37-47. doi: 10.22059/jac.2018.69503
