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2007 | 27 | 2 | 251-268
Tytuł artykułu

Further results on sequentially additive graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a graph G with p vertices, q edges and a positive integer k, a k-sequentially additive labeling of G is an assignment of distinct numbers k,k+1,k+2,...,k+p+q-1 to the p+q elements of G so that every edge uv of G receives the sum of the numbers assigned to the vertices u and v. A graph which admits such an assignment to its elements is called a k-sequentially additive graph. In this paper, we give an upper bound for k with respect to which the given graph may possibly be k-sequentially additive using the independence number of the graph. Also, we prove a variety of results on k-sequentially additive graphs, including the number of isolated vertices to be added to a complete graph with four or more vertices to be simply sequentially additive and a construction of an infinite family of k-sequentially additive graphs from a given k-sequentially additive graph.
Wydawca
Rocznik
Tom
27
Numer
2
Strony
251-268
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-01-04
poprawiono
2007-02-05
zaakceptowano
2007-02-05
Twórcy
  • Department of mathematical and Computational sciences, National Institute of Technology Karnataka, Surathkal, Srinivasnagar-575025, India
autor
  • School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan NSW 2308, Australia
Bibliografia
  • [1] B.D. Acharya and S.M. Hegde, Arithmetic graphs, J. Graph Theory 14 (1990) 275-299, doi: 10.1002/jgt.3190140302.
  • [2] B.D. Acharya and S.M. Hegde, Strongly indexable graphs, Discrete Math. 93 (1991) 123-129, doi: 10.1016/0012-365X(91)90248-Z.
  • [3] D.W. Bange, A.E. Barkauskas and P.J. Slater, Sequentially additive graphs, Discrete Math. 44 (1983) 235-241, doi: 10.1016/0012-365X(83)90187-5.
  • [4] G.S. Bloom, Numbered undirected graphs and their uses: A survey of unifying scientific and engineering concepts and its use in developing a theory of non-redundant homometric sets relating to some ambiguities in x-ray diffraction analysis (Ph. D., dissertation, Univ. of Southern California, Loss Angeles, 1975).
  • [5] Herbert B. Enderton, Elements of Set Theory (Academic Press, 2006).
  • [6] H. Enomoto, H. Liadi, A.S.T. Nakamigava and G. Ringel, Super edge magic graphs, SUT J. Mathematics 34 (2) (1998) 105-109.
  • [7] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Combinatorics DS#6 (2003) 1-148.
  • [8] S.W. Golomb, How to number a graph, in: Graph Theory and Computing, (ed. R.C. Read) (Academic Press, 1972), 23-37.
  • [9] F. Harary, Graph Theory (Addison Wesley, Reading, Massachusetts, 1969).
  • [10] S.M. Hegde, On indexable graphs, J. Combin., Information & System Sciences 17 (1992) 316-331.
  • [11] S.M. Hegde and Shetty Sudhakar, Strongly k-indexable labelings and super edge magic labelings are equivalent, NITK Research Bulletin 12 (2003) 23-28.
  • [12] A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs, Proceedings of the International Symposium, Rome (ed. P. Rosentiehl) (Dunod, Paris, 1981) 349-355.
  • [13] D.B. West, Introduction to Graph Theory (Prentice Hall of India, New Delhi, 2003).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1359
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