%0 Journal Article %T Snakes and Caterpillars in Graceful Graphs %J Journal of Algorithms and Computation %I University of Tehran %Z 2476-2776 %A Barrientos, Christian %A Minion, Sarah M %D 2018 %\ 12/30/2018 %V 50 %N issue 2 %P 37-47 %! Snakes and Caterpillars in Graceful Graphs %K \a-labeling %K graceful labeling %K snake %K caterpillar. & & \\ %\vspace{0.1cm} \end{tabular} %R 10.22059/jac.2018.69503 %X 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 thelarger stable sets, in both caterpillars, have the same cardinality. We studythe conditions that allow us to replace, within a gracefully labeled graph,some snakes (or paths) by analogous caterpillars, to produce a new gracefulgraph. We present five families of graphs where this replacement isfeasible, generalizing in this way some existing results: subdivided trees, first attachment trees, path-like trees, two-point union of paths, and armed crowns. %U https://jac.ut.ac.ir/article_69503_bd9e68d1fedd8b959976b68013ae5357.pdf