Math

On The Structure of Path-like Trees F. A. Muntaner-Batle Facultat de Ci`ncies Pol´ e ?tiques i Jur´ ?diques Universitat Internacional de Catalunya, c/ Immaculada 22 08017 Barcelona, Spain. M. Rius-Font Departament de Matem`tica Aplicada i Telem`tica a a Universitat Polit`cnica de Catalunya, Jordi Girona Salgado 1 e 08034 Barcelona, Spain. ? Mathematics theater Classi?cations: 05C05, 05C78 Abstract We study the embodied coordinate of avenue-like trees. In watch to do this, we introduce a square off of trees that we band expandable trees. In this cornerstone we also reason forth the concept of track-like trees and we call much(prenominal) abstractedness generalized path-like trees. As in the case of path-like trees, generalized path-like trees, grant very mincing labeling properties. get a line words: Tree, path-like tree, Tp -tree, expandable tree, ?-valuation, tops(predicate) black eye into-magic labeling, special super edge-magic labeling, harmonised labeling, super-edge antimagic labeling. 1 Introduction For the unde?ned concepts and notation, the reader is directed to both [4] or [6]. This paper is in general devoted to study the structure of a peculiar(prenominal) family of trees called path-like trees. Path-like trees were ?rst introduced by Barrientos in [3] in his e?ort to ?nd families of trees with straight-laced labeling properties.

They are de?ned as follows: Supported by the Spanish query Council under(a)(a) project MTM2004-07891-C02-01 and by the Catalan Research Council under project 2001SGR00258. ? 1 We embed the path Pn as a subgraph of the 2-dimensional grid, that is to regulate the graph Pk × Pl . Given such(prenominal) an embedding, we consider the ordered gage of subpaths P1 , P2 , . . . , Pm which are maximum straight segments in the embedding, and such that the end of Li is the first-class honours degree of Li+1 . conceive that Li ? P2 for some i and that = some flush u of Li?1 is at distance 1 in the grid to a vertex v of Li+1 . An elementary transformation of the path consists in replacing the edge of Li by a new edge uv. We assure that a tree T...If you deprivation to get a across-the-board essay, order it on our website: Ordercustompaper.com

If you want to get a full essay, wisit our page: write my paper