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Year 2015, Volume: 5 Issue: 2, 269 - 275, 01.12.2015

Abstract

References

  • Gallian,J.A., (2013), A dynamic survey of graph labeling, Electronic Journal of Combinatorics, DS6, Sixteenth edition, url:http://www.combinatorics.org/Surveys/.
  • Hrnciar,P. and Havier,A., (2001), All Trees of Diameter Five Are Graceful, Discrete Mathematics, 233, pp. 133-150.
  • Mishra,D. and Panda,A.C., (2013), Some New Transformations And Their Applications Involving Graceful Tree Labeling, International Journal of Mathematical Sciences and Engineering Aplications, Vol.7, No.1, pp. 239-254.
  • Mishra,D. and Panigrahi,P., (2008), Some Graceful Lobsters with All Three Types of Branches In- cident on the Vertices of the Central Path, Computers and Mathematics with Applications 56, pp. 1382-1394.
  • Rosa,A., (1968), On certain valuations of the vertices of a graph, in The´orie des Graphes, (ed. P. Rosenstiehl), Dunod, Paris, pp. 349-355, MR 36-6319.
  • Sethuraman,G. and Jesintha,J., (2009), All banana trees are graceful, Advances Appl. Disc. Math., 4, pp. 53-64.

Some New Classes Of Graceful Diameter Six Trees

Year 2015, Volume: 5 Issue: 2, 269 - 275, 01.12.2015

Abstract

Here we denote a diameter six tree by a0; a1, a2, . . . , am; b1, b2, . . . , bn; c1, c2, . . . , cr , where a0 is the center of the tree; ai, i = 1, 2, . . . , m, bj , j = 1, 2, . . . , n, and ck, k = 1, 2, . . . , r are the vertices of the tree adjacent to a0; each ai is the center of a diameter four tree, each bj is the center of a star, and each ck is a pendant vertex. Here we give graceful labelings to some new classes of diameter six trees a0; a1, a2, . . . , am; b1, b2, . . . , bn; c1, c2, . . . , cr in which the branches of a diameter four tree incident on a0 are of same type, i.e. either they are all odd branches or even branches. Here by a branch we mean a star, i.e. we call a star an odd branch if its center has an odd degree and an even branch if its center has an even degree

References

  • Gallian,J.A., (2013), A dynamic survey of graph labeling, Electronic Journal of Combinatorics, DS6, Sixteenth edition, url:http://www.combinatorics.org/Surveys/.
  • Hrnciar,P. and Havier,A., (2001), All Trees of Diameter Five Are Graceful, Discrete Mathematics, 233, pp. 133-150.
  • Mishra,D. and Panda,A.C., (2013), Some New Transformations And Their Applications Involving Graceful Tree Labeling, International Journal of Mathematical Sciences and Engineering Aplications, Vol.7, No.1, pp. 239-254.
  • Mishra,D. and Panigrahi,P., (2008), Some Graceful Lobsters with All Three Types of Branches In- cident on the Vertices of the Central Path, Computers and Mathematics with Applications 56, pp. 1382-1394.
  • Rosa,A., (1968), On certain valuations of the vertices of a graph, in The´orie des Graphes, (ed. P. Rosenstiehl), Dunod, Paris, pp. 349-355, MR 36-6319.
  • Sethuraman,G. and Jesintha,J., (2009), All banana trees are graceful, Advances Appl. Disc. Math., 4, pp. 53-64.
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Details

Primary Language English
Journal Section Research Article
Authors

A. C. Panda This is me

D. Mishra This is me

Publication Date December 1, 2015
Published in Issue Year 2015 Volume: 5 Issue: 2

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