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Snakes and Caterpillars in Graceful Graphs | ||
| Journal of Algorithms and Computation | ||
| مقاله 3، دوره 50، issue 2، اسفند 2018، صفحه 37-47 اصل مقاله (762.65 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jac.2018.69503 | ||
| نویسندگان | ||
| Christian Barrientos* 1؛ Sarah M Minion2 | ||
| 1Department of Mathematics, Valencia College, Orlando, FL, 32825, USA. | ||
| 2Department of Mathematics, Valencia College, Orlando, FL, 32825, USA | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| \a-labeling؛ graceful labeling؛ snake؛ caterpillar. & & \\ %\vspace{0.1cm} \end{tabular} | ||
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