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Year 2019, Volume 9, Issue 4, 693 - 703, 01.12.2019

Abstract

References

  • Ahmad, A., Baig, A. Q., and Imran, M., On super edge-magicness of graphs, Utilitas Math. to appear.
  • Baˇca, M., Dafik, Miller, M., and Ryan, J., (2008), Edge-antimagic total labeling of disjoint unions of caterpillars, J. Comb. Math. Comb. Computing, 65, pp. 61–70.
  • Baˇca, M., Y. Lin, Y., Miller, M., and Simanjuntak, R., (2001), New constructions of magic and antimagic graph labelings, Utilitas Math., 60, pp. 229–239.
  • Baˇca, M., Lin, Y. and Muntaner-Batle, F.A., (2007), Super edge-antimagic labelings of the path-like trees, Utilitas Math.,73, pp. 117–128.
  • Baˇca, M., and M. Miller, M., (2008), Super Edge-Antimagic Graphs, Brown Walker Press, Boca Raton, Florida USA.
  • Baˇca, M.,, Lin, Y., Miller, M., and M. Z. Youssel, M. Z., Edge-antimagic graphs, Discrete Math., to appear.
  • Baskoro, E. T., and Cholily. Y., (2004), Expanding super edge-magic graphs, Proc. ITB Sains and Tek.,36:2, pp. 117–125.
  • Enomoto, H., Llado, A. S., Nakamigawa, T., and Ringle, G., (1980), Super edge-magic graphs, SUT J. Math., 34, pp. 105–109.
  • Figueroa-Centeno, R. M., Ichishima, R., and Muntaner-Batle, F. A., (2001), The place of super edge- magic labeling among other classes of labeling, Discrete Math., 231, pp. 153–168.
  • Figueroa-Centeno, R. M., Ichishima, R., and Muntaner-Batle, F. A., (2002), On super edge-magic graphs, Ars Combin., 64, pp. 81–95.
  • Figueroa-Centeno, R. M., Ichishima, R., and Mantaner-Batle, F. A., (2005), On edge-magic labeling of certain disjoint union graphs, Australas. J. Combin., 32, pp. 225–242.
  • Fukuchi, Y., A recursive theorem for super edge-magic labeling of trees, (2000), SUT J. Math., 36, pp. 279–285.
  • J. A. Gallian, (2009), A dynamic survey of graph labeling, Electronic J. Combin.
  • Hussain, M., Baskoro, E. T., Slamin, (2009) On super edge-magic total labeling of banana trees, Utilitas Math., 79, pp. 243–251.
  • Javaid, M., (2014), On super edge-antimagic total labeling of generalized extended w-trees, Interna- tional Journl of Mathematics and soft Computing, 4, pp. 17–25.
  • A. Kotzig, A., and Rosa, A., (1970), Magic valuations of finite graphs, Canad. Math. Bull., 13, pp. 451–461.
  • Kotzig, A., and Rosa, A Magic valuation of complete graphs, (1972), Centre de Recherches Mathe- matiques, Universite de Montreal, CRM–175.
  • Lee, S. M., and Shah, Q. X., All trees with at most 17 vertices are super edge-magic, (2002), 16th MCCCC Conference, Carbondale, University Southern Illinois.
  • Raheem, A., Javaid, M., Baig, A. Q., (2016), Antimagic labeling of the union of subdivided stars, TWMS J. App. Eng. Math.,6(2), pp.244–250.
  • Raheem, A., Javaid, M., Baig, A. Q., (2016), On antimagicness of generalized extene w-trees, science Internation Journal, 28(5),pp. 5057–5022.
  • Raheem, A., (2018), On super (a, d)-edge antimagic total labeling of a subdivided stars, Ars Combin., 136, pp. 169–179.
  • K. A. Sugeng. K. A., Miller, M., Baca, M., (a, d)-edge-antimagic total labeling of caterpillars, (2005), Lecture Notes Comput. Sci., 3330 pp. 169–180.
  • West, D. B.,(1996), An Introduction to Graph Theory, Prentice-Hall.

ON SUPER a; d -EAT VALUATION OF SUBDIVIDED CATERPILLAR

Year 2019, Volume 9, Issue 4, 693 - 703, 01.12.2019

Abstract

Let G = V G , E G be a graph with v = |V G | vertices and e = |E G | edges. A bijective function λ : V G ∪ E G ↔ {1, 2, . . . , v + e} is called an a, d - edge antimagic total EAT labeling valuation if the weight of all the edges {w xy : xy ∈ E G } form an arithmetic sequence starting with first term a and having common difference d, where w xy = λ x + λ y + λ xy . And, if λ V = {1, 2, . . . , v} then G is super a, d -edge antimagic total EAT graph. In this paper, we determine the super a,d -edge antimagic total EAT labeling of the subdivided caterpillar for different values of the parameter d.

References

  • Ahmad, A., Baig, A. Q., and Imran, M., On super edge-magicness of graphs, Utilitas Math. to appear.
  • Baˇca, M., Dafik, Miller, M., and Ryan, J., (2008), Edge-antimagic total labeling of disjoint unions of caterpillars, J. Comb. Math. Comb. Computing, 65, pp. 61–70.
  • Baˇca, M., Y. Lin, Y., Miller, M., and Simanjuntak, R., (2001), New constructions of magic and antimagic graph labelings, Utilitas Math., 60, pp. 229–239.
  • Baˇca, M., Lin, Y. and Muntaner-Batle, F.A., (2007), Super edge-antimagic labelings of the path-like trees, Utilitas Math.,73, pp. 117–128.
  • Baˇca, M., and M. Miller, M., (2008), Super Edge-Antimagic Graphs, Brown Walker Press, Boca Raton, Florida USA.
  • Baˇca, M.,, Lin, Y., Miller, M., and M. Z. Youssel, M. Z., Edge-antimagic graphs, Discrete Math., to appear.
  • Baskoro, E. T., and Cholily. Y., (2004), Expanding super edge-magic graphs, Proc. ITB Sains and Tek.,36:2, pp. 117–125.
  • Enomoto, H., Llado, A. S., Nakamigawa, T., and Ringle, G., (1980), Super edge-magic graphs, SUT J. Math., 34, pp. 105–109.
  • Figueroa-Centeno, R. M., Ichishima, R., and Muntaner-Batle, F. A., (2001), The place of super edge- magic labeling among other classes of labeling, Discrete Math., 231, pp. 153–168.
  • Figueroa-Centeno, R. M., Ichishima, R., and Muntaner-Batle, F. A., (2002), On super edge-magic graphs, Ars Combin., 64, pp. 81–95.
  • Figueroa-Centeno, R. M., Ichishima, R., and Mantaner-Batle, F. A., (2005), On edge-magic labeling of certain disjoint union graphs, Australas. J. Combin., 32, pp. 225–242.
  • Fukuchi, Y., A recursive theorem for super edge-magic labeling of trees, (2000), SUT J. Math., 36, pp. 279–285.
  • J. A. Gallian, (2009), A dynamic survey of graph labeling, Electronic J. Combin.
  • Hussain, M., Baskoro, E. T., Slamin, (2009) On super edge-magic total labeling of banana trees, Utilitas Math., 79, pp. 243–251.
  • Javaid, M., (2014), On super edge-antimagic total labeling of generalized extended w-trees, Interna- tional Journl of Mathematics and soft Computing, 4, pp. 17–25.
  • A. Kotzig, A., and Rosa, A., (1970), Magic valuations of finite graphs, Canad. Math. Bull., 13, pp. 451–461.
  • Kotzig, A., and Rosa, A Magic valuation of complete graphs, (1972), Centre de Recherches Mathe- matiques, Universite de Montreal, CRM–175.
  • Lee, S. M., and Shah, Q. X., All trees with at most 17 vertices are super edge-magic, (2002), 16th MCCCC Conference, Carbondale, University Southern Illinois.
  • Raheem, A., Javaid, M., Baig, A. Q., (2016), Antimagic labeling of the union of subdivided stars, TWMS J. App. Eng. Math.,6(2), pp.244–250.
  • Raheem, A., Javaid, M., Baig, A. Q., (2016), On antimagicness of generalized extene w-trees, science Internation Journal, 28(5),pp. 5057–5022.
  • Raheem, A., (2018), On super (a, d)-edge antimagic total labeling of a subdivided stars, Ars Combin., 136, pp. 169–179.
  • K. A. Sugeng. K. A., Miller, M., Baca, M., (a, d)-edge-antimagic total labeling of caterpillars, (2005), Lecture Notes Comput. Sci., 3330 pp. 169–180.
  • West, D. B.,(1996), An Introduction to Graph Theory, Prentice-Hall.

Details

Primary Language English
Journal Section Research Article
Authors

A. RAHEEM This is me
Department of Mathematics, National University of Singapore, Singapore, 119076.


M. JAVAİD This is me
Department of Mathematics, School of Science, University of Management and Technology, Pakistan.


M. A. UMAR This is me
Department of Mathematics, Govenment Degree Boys College (B), Sharqpur Shareef, Pakistan.


G. C. LAU This is me
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Johor, Segamat, Malaysia.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760937, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {693 - 703}, title = {ON SUPER a; d -EAT VALUATION OF SUBDIVIDED CATERPILLAR}, key = {cite}, author = {Raheem, A. and Javaid, M. and Umar, M. A. and Lau, G. C.} }