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Year 2019, Volume 9, Issue 4, 930 - 935, 01.12.2019

Abstract

References

  • Cockayne, E. J. and Hedetniemi, S. T., (1977), Towards a theory of domination in graphs, Networks, 7, pp. 247–261.
  • Cuaresma, E. C. Jr. and Paluga, R. N., (2015), On the hub number of some graphs, Annals of Studies in Science and Humanities, 1(1), pp. 17–24.
  • Frucht, R. and Harary, F., (1970), On the corona of two graphs, Aequat Math., 4, pp. 322–325.
  • Harary, F., (1969), Graph Theory. Addison Wesley, Reading Mass.
  • Haynes, T. W., Hedetniemi, S. T. and Slater, P. J., (1998), Fundamentals of Domination in Graphs, Marcel Dekker, Inc.
  • Khalaf, S. I., Mathad, V. and Mahde, S. S., (2018), Hubtic number in graphs, Opuscula Math., 38(6), pp. 841–847.
  • Khalaf, S. I., Mathad, V. and Mahde, S. S., (2018), Edge hubtic number in graphs, Int. J. Math. Combin., 3, pp. 141–146.
  • Khalaf, S. I. and Mathad, V., (2019), Restrained hub number in graphs, Bull. Int. Math. Virtual Inst., 9, pp. 103–109.
  • Mahde, S. S., Mathad, V. and Sahal, A. M., (2015), Hub-integrity of graphs, Bull. Int. Math. Virtual Inst., 5, pp. 57–64.
  • Mahde, S. S. and Mathad, V., (2016), Some results on the edge hub-integrity of graphs, Asia Pacific Journal of Mathematics, 3(2), pp. 173–185.
  • Mahde, S. S. and Mathad, V., (2018), Hub-integrity of line graph, Electron. J. Math. Anal. Appl., 6, pp. 255–265.
  • Mathad, V., Sahal, A. M. and Kiran S., (2014), The total hub number of graphs, Bull. Int. Math. Virtual Inst., 4, pp. 61–67.
  • Walsh, M., (2006), The hub number of a graph, Int. J. Mathematics and Computer Science, 1, pp. 117–124.

ON HUBTIC AND RESTRAINED HUBTIC OF A GRAPH

Year 2019, Volume 9, Issue 4, 930 - 935, 01.12.2019

Abstract

In this article, the hubtic number of the join and corona of two connected graphs is computed. The restrained hubtic number r G of a graph G is the maximum number such that we can partition V G into pairwise disjoint restrained hub sets. We compute the restrained hubtic number of some standard graphs. Some bounds for r G are obtained.

References

  • Cockayne, E. J. and Hedetniemi, S. T., (1977), Towards a theory of domination in graphs, Networks, 7, pp. 247–261.
  • Cuaresma, E. C. Jr. and Paluga, R. N., (2015), On the hub number of some graphs, Annals of Studies in Science and Humanities, 1(1), pp. 17–24.
  • Frucht, R. and Harary, F., (1970), On the corona of two graphs, Aequat Math., 4, pp. 322–325.
  • Harary, F., (1969), Graph Theory. Addison Wesley, Reading Mass.
  • Haynes, T. W., Hedetniemi, S. T. and Slater, P. J., (1998), Fundamentals of Domination in Graphs, Marcel Dekker, Inc.
  • Khalaf, S. I., Mathad, V. and Mahde, S. S., (2018), Hubtic number in graphs, Opuscula Math., 38(6), pp. 841–847.
  • Khalaf, S. I., Mathad, V. and Mahde, S. S., (2018), Edge hubtic number in graphs, Int. J. Math. Combin., 3, pp. 141–146.
  • Khalaf, S. I. and Mathad, V., (2019), Restrained hub number in graphs, Bull. Int. Math. Virtual Inst., 9, pp. 103–109.
  • Mahde, S. S., Mathad, V. and Sahal, A. M., (2015), Hub-integrity of graphs, Bull. Int. Math. Virtual Inst., 5, pp. 57–64.
  • Mahde, S. S. and Mathad, V., (2016), Some results on the edge hub-integrity of graphs, Asia Pacific Journal of Mathematics, 3(2), pp. 173–185.
  • Mahde, S. S. and Mathad, V., (2018), Hub-integrity of line graph, Electron. J. Math. Anal. Appl., 6, pp. 255–265.
  • Mathad, V., Sahal, A. M. and Kiran S., (2014), The total hub number of graphs, Bull. Int. Math. Virtual Inst., 4, pp. 61–67.
  • Walsh, M., (2006), The hub number of a graph, Int. J. Mathematics and Computer Science, 1, pp. 117–124.

Details

Primary Language English
Journal Section Research Article
Authors

S. I. KHALAF This is me
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru, India.


V. MATHAD This is me
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru, India.

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

Cite

Bibtex @ { twmsjaem760966, 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 = {930 - 935}, title = {ON HUBTIC AND RESTRAINED HUBTIC OF A GRAPH}, key = {cite}, author = {Khalaf, S. I. and Mathad, V.} }