%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