ON THE STRUCTURE OF PATH-LIKE TREES

 F.A. Muntaner-Batle Facultat de Ciències Polítiques i Jurídiques Universitat Internacional de Catalunya c/ Immaculada 22, 08017 Barcelona, Spain e-mail: famb1es@yahoo.es Miquel Rius-Font Departament de Matemàtica Aplicada i Telemàtica Universitat Politècnica de Catalunya Jordi Girona Salgado 1, 08034 Barcelona, Spain

Abstract

We study the structure of path-like trees. In order to do this, we introduce a set of trees that we call expandable trees. In this paper we also generalize the concept of path-like trees and we call such generalization generalized path-like trees. As in the case of path-like trees, generalized path-like trees, have very nice labeling properties.

Keywords: tree, path-like tree, Tp-tree, expandable tree, α-valuation, super edge-magic labeling, special super edge-magic labeling, harmonious labeling, super edge-antimagic labeling.

2000 Mathematics Subject Classifications: 05C05, 05C78.

References

 [1] B.D. Acharya, Elementary parallel transforamtions of graphs, AKCE International J. Graphs and Combin. 1 (2004) 63-67. [2] M. Bača, Y. Lin and F.A. Muntaner-Batle, Super edge-antimagic labelings of the path-like trees, Utilitas Math., to appear. [3] M. Bača, Y. Lin and F.A. Muntaner-Batle, Normalized embeddings of path-like treess, Utilitas Math. 73 (2007) 117-128. [4] C. Barrientos, Difference Vertex Labelings, Ph.D. Thesis (Universitat Politècnica de Catalunya, 2004). [5] G. Chartrand and L. Lesniak, Graphs and Digraphs, second edition (Wadsworth & Brooks/Cole Advanced Books and Software, Monterey, 1986). [6] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, On super edge-magic graphs, Ars Combin. 64 (2002) 81-95. [7] J.A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics DS6 (2000). [8] R.L. Graham and N.J. Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Math. 1 (1980) 382-404, doi: 10.1137/0601045. [9] S.M. Hegde and S. Shetty, On graceful trees, Appl. Math. E-Notes 2 (2002) 192-197. [10] F.A. Muntaner-Batle, Special super edge-magic labelings of bipartite graphs, J. Combin. Math. Combin. Comput. 39 (2001) 107-120. [11] A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs, Internat. Symposium, Rome, July 1966 (Gordon and Breach, N.Y. and Dunot, Paris, 1967) 349-355.

Received 23 May 2007
Revised 6 March 2008
Accepted 6 March 2008