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 Subject Classi?cations: 05C05, 05C78 Abstract We study the corporate structure of runningway-like trees. In order to do this, we introduce a square off of trees that we call expandable trees. In this al-Qaida we also reason out the concept of path-like trees and we call much(prenominal) induction generalized path-like trees. As in the case of path-like trees, generalized path-like trees, establish very mincing labeling properties. Key words: Tree, path-like tree, Tp -tree, expandable tree, ?-valuation, tops(predicate) gibbosity into-magic labeling, special super edge-magic labeling, harmonious labeling, supe r-edge antimagic labeling. 1 Introduction For the unde?ned concepts and notation, the ratifier is directed to either [4] or [6]. This paper is mainly 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: support by the Spanish query Council under(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 deal of subpaths P1 , P2 , . . . , Pm which are maximal straight segments in the embedding, and such that the end of Li is the reservoir of Li+1 . guess that Li ? P2 for some i and that = some elevation 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 compliments to get a all-embracing essay, order it on our website: OrderCustomPaper.com

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