Research Article
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Year 2023, , 16 - 26, 15.10.2023

Yaşar Nacaroğlu

https://doi.org/10.33773/jum.1333260

Abstract

References

  • N. Akgunes, K.C. Das, A.S. Cevik and I.N. Cangul, Some properties on the lexicographic product of graphs obtained by monogenic semigroups, Journal of Inequalities and Applications, Vol.238, pp.1-9 (2013).
  • N. Akgunes, Y. Nacaroglu, S. Pak, Line Graphs of Monogenic Semigroup Graphs, Journal of Mathematics, Vol.2021, Article ID 6630011, 4 pages (2021).
  • N.Akgunes, K.C.Das, A.S.Cevik, Topological indices on a graph of monogenic semigroups, Topics in Chemical Graph Theory(Book Chapter), pp.3-20 (2014).
  • D.D. Anderson and M. Naseer, Beck's coloring of a commutative ring, Journal of Algebra, Vol.159, pp.500-514 (1993).
  • D.F. Anderson and P.S. Livingston, The zero-divisor graph of commutative ring, Journal of Algebra, Vol.217, pp.434-447 (1999).
  • DF. Anderson, T. Asir, A. Badawi, T. Tamizh Chelvam, Graphs from rings, 1st edn. Springer, Berlin (2021).
  • B.Basavanagoud and E.Chitra1, On leap Zagreb indices of some nanostructures, Malaya Journal of Matematik, Vol.6,N.4, pp.816-822 (2018).
  • I. Beck, Coloring of commutating ring, Journal of Algebra, Vol.116, pp.208-226 (1988).
  • N. Chidambaram, S. Mohandoss, X. Yu, X. Zhang, On leap Zagreb indices of bridge and chain graphs, AIMS Mathematics, Vol.5,N.6, pp.6521-6536 (2020).
  • K.C. Das, N. Akgunes and A.S. Cevik, On a graph of monogenic semigroup, Journal of Inequalities and Applications, Vol.2013,N.44, pp.1-13 (2013).
  • F.R. DeMeyer, T. McKenzie and K. Schneider, The zero-divisor graph of a commutative semigroup, Semigroup Forum, Vol.65, pp.206-214 (2002).
  • J. Devillers, and A. T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR, Amsterdam: Gordon and Breach 1999," Journal of Chemical Information and Computer Sciences, Vol. 42,N.6: 1507 (2002).
  • J.L. Gross and J. Yellen, eds. Handbook of graph theory, CRC press (2003).
  • I. Gutman, N. Trinajsti_c, Graph theory and molecular orbitals. Total '-electron energy of alternant hydrocarbons, Chemical Physics Letters, Vol.17, N.4, pp.535-538 (1972).
  • I. Gutman, B. Rucic, N. Trinajsti´c, and C. F. Wilcox, \Graph theory and molecular orbitals. XII. Acyclic polyenes" ,-e Journal of Chemical Physics, Vol.62,N.9, pp.3399{3405 (1975).
  • R.S. Haoer, M.A. Mohammed, N. Chidambaram, On leap eccentric connectivity index of thorny graphs, Eurasian Chemical Communications, Vol.2, pp.1033-1039 (2020).
  • V. R. Kulli, On F-leap indices and F-leap polynomials of some graphs, International Journal of Mathematical Archive, Vol.9, pp. 41{49 (2018).
  • H.R. Manjunathe, A.M. Naji, P. Shiladhar, N.D. Soner, Leap eccentric connectivity index of some graph operations International Journal of Research and Analytical Reviews, Vol.6,N.1, pp.882-887 (2019).
  • Y. Nacaroğlu, On Join Operation of Graphs by Obtained Monogenic Semigroups, Turkish Journal of Mathematics and Computer Science, Vol.13,N.1, pp.57-62 (2021).
  • Y. Nacaroğlu, On the corona product of monogenic semigroup graphs, Advances and Applications in Discrete Mathematics, Vol.19, pp.409-420 (2018).
  • Y. Nacaroğlu and N. Akgüneş, On the sigma index of the corona products of monogenic semigroup graphs, Journal of Universal Mathematics, Vol.2,N.1, pp.68-74 (2019).
  • A.M.Naji1, N.D. Soner1and, I. Gutman, On leap Zagreb indices of graphs , Communications in Combinatorics and Optimization, Vol.2,N.2, pp.99-117 (2017).
  • S. Pawar, A.M. Naji, N.D. Soner, I.N. Cangul, On leap eccentric connectivity index of graphs, https://avesis.uludag.edu.tr/yayin/65f71f1f-82bc-4e6b-8109-30c70cc1b456/onleap-eccentric-connectivity-index-of-graphs/document.pdf.
  • H.S. Ramane and K.S. Pise, New Results on Leap Zagreb Indices, Annals of Mathematics and Computer Science, Vol.15, pp.20-30 (2023).
  • N.D. Soner and A. M. Naji, The k-distance neighborhood polynomial of a graph, World Academy Sci.Engin. Tech. Conference Proceedings, San Francico, USA, Sep 26-27, 18(9), part XV 2359-2364 (2016).
  • L. Song, H. Liu and Z. Tang, Some properties of the leap eccentric connectivity index of graphs, Iranian Journal of Mathematical Chemistry, Vol.11,N.4, pp.227-237 (2020).
  • S. Sowmya, On leap eccentric connectivity index of transformation graphs of a path (hydrogen detected alkanes) Advances and Applications in Discrete Mathematics, Vol.27, pp.123-140 (2021).
  • J.M. Zhu, N. Dehgardi, X. Li, The Third Leap Zagreb Index for Trees, Journal of Chemistry, Vol.2019, Article ID 9296401, 6 pages (2019).

ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS

Year 2023, , 16 - 26, 15.10.2023

Yaşar Nacaroğlu

https://doi.org/10.33773/jum.1333260

Abstract

In 2013, Das et al. defined the monogenic semigroup graphs [10]. And, various topological indices of the monogenic semigroup graphs have been calculated so far [3,21]. The aim of this study is to continue to create formulas for the topological indices of these special graphs. In this study, we give exact formulae for various the leap Zagreb indices of this special algebraic graph obtained from monogenic semigroups.

Keywords

Topological indices Leap Zagreb indices Monogenic semigroup graphs

References

  • N. Akgunes, K.C. Das, A.S. Cevik and I.N. Cangul, Some properties on the lexicographic product of graphs obtained by monogenic semigroups, Journal of Inequalities and Applications, Vol.238, pp.1-9 (2013).
  • N. Akgunes, Y. Nacaroglu, S. Pak, Line Graphs of Monogenic Semigroup Graphs, Journal of Mathematics, Vol.2021, Article ID 6630011, 4 pages (2021).
  • N.Akgunes, K.C.Das, A.S.Cevik, Topological indices on a graph of monogenic semigroups, Topics in Chemical Graph Theory(Book Chapter), pp.3-20 (2014).
  • D.D. Anderson and M. Naseer, Beck's coloring of a commutative ring, Journal of Algebra, Vol.159, pp.500-514 (1993).
  • D.F. Anderson and P.S. Livingston, The zero-divisor graph of commutative ring, Journal of Algebra, Vol.217, pp.434-447 (1999).
  • DF. Anderson, T. Asir, A. Badawi, T. Tamizh Chelvam, Graphs from rings, 1st edn. Springer, Berlin (2021).
  • B.Basavanagoud and E.Chitra1, On leap Zagreb indices of some nanostructures, Malaya Journal of Matematik, Vol.6,N.4, pp.816-822 (2018).
  • I. Beck, Coloring of commutating ring, Journal of Algebra, Vol.116, pp.208-226 (1988).
  • N. Chidambaram, S. Mohandoss, X. Yu, X. Zhang, On leap Zagreb indices of bridge and chain graphs, AIMS Mathematics, Vol.5,N.6, pp.6521-6536 (2020).
  • K.C. Das, N. Akgunes and A.S. Cevik, On a graph of monogenic semigroup, Journal of Inequalities and Applications, Vol.2013,N.44, pp.1-13 (2013).
  • F.R. DeMeyer, T. McKenzie and K. Schneider, The zero-divisor graph of a commutative semigroup, Semigroup Forum, Vol.65, pp.206-214 (2002).
  • J. Devillers, and A. T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR, Amsterdam: Gordon and Breach 1999," Journal of Chemical Information and Computer Sciences, Vol. 42,N.6: 1507 (2002).
  • J.L. Gross and J. Yellen, eds. Handbook of graph theory, CRC press (2003).
  • I. Gutman, N. Trinajsti_c, Graph theory and molecular orbitals. Total '-electron energy of alternant hydrocarbons, Chemical Physics Letters, Vol.17, N.4, pp.535-538 (1972).
  • I. Gutman, B. Rucic, N. Trinajsti´c, and C. F. Wilcox, \Graph theory and molecular orbitals. XII. Acyclic polyenes" ,-e Journal of Chemical Physics, Vol.62,N.9, pp.3399{3405 (1975).
  • R.S. Haoer, M.A. Mohammed, N. Chidambaram, On leap eccentric connectivity index of thorny graphs, Eurasian Chemical Communications, Vol.2, pp.1033-1039 (2020).
  • V. R. Kulli, On F-leap indices and F-leap polynomials of some graphs, International Journal of Mathematical Archive, Vol.9, pp. 41{49 (2018).
  • H.R. Manjunathe, A.M. Naji, P. Shiladhar, N.D. Soner, Leap eccentric connectivity index of some graph operations International Journal of Research and Analytical Reviews, Vol.6,N.1, pp.882-887 (2019).
  • Y. Nacaroğlu, On Join Operation of Graphs by Obtained Monogenic Semigroups, Turkish Journal of Mathematics and Computer Science, Vol.13,N.1, pp.57-62 (2021).
  • Y. Nacaroğlu, On the corona product of monogenic semigroup graphs, Advances and Applications in Discrete Mathematics, Vol.19, pp.409-420 (2018).
  • Y. Nacaroğlu and N. Akgüneş, On the sigma index of the corona products of monogenic semigroup graphs, Journal of Universal Mathematics, Vol.2,N.1, pp.68-74 (2019).
  • A.M.Naji1, N.D. Soner1and, I. Gutman, On leap Zagreb indices of graphs , Communications in Combinatorics and Optimization, Vol.2,N.2, pp.99-117 (2017).
  • S. Pawar, A.M. Naji, N.D. Soner, I.N. Cangul, On leap eccentric connectivity index of graphs, https://avesis.uludag.edu.tr/yayin/65f71f1f-82bc-4e6b-8109-30c70cc1b456/onleap-eccentric-connectivity-index-of-graphs/document.pdf.
  • H.S. Ramane and K.S. Pise, New Results on Leap Zagreb Indices, Annals of Mathematics and Computer Science, Vol.15, pp.20-30 (2023).
  • N.D. Soner and A. M. Naji, The k-distance neighborhood polynomial of a graph, World Academy Sci.Engin. Tech. Conference Proceedings, San Francico, USA, Sep 26-27, 18(9), part XV 2359-2364 (2016).
  • L. Song, H. Liu and Z. Tang, Some properties of the leap eccentric connectivity index of graphs, Iranian Journal of Mathematical Chemistry, Vol.11,N.4, pp.227-237 (2020).
  • S. Sowmya, On leap eccentric connectivity index of transformation graphs of a path (hydrogen detected alkanes) Advances and Applications in Discrete Mathematics, Vol.27, pp.123-140 (2021).
  • J.M. Zhu, N. Dehgardi, X. Li, The Third Leap Zagreb Index for Trees, Journal of Chemistry, Vol.2019, Article ID 9296401, 6 pages (2019).
There are 28 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory, Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)
Journal Section Research Article
Authors

Yaşar Nacaroğlu 0000-0001-7179-0490

Publication Date October 15, 2023
Submission Date July 26, 2023
Acceptance Date October 6, 2023
Published in Issue Year 2023

Cite

APA Nacaroğlu, Y. (2023). ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS. Journal of Universal Mathematics, 6(3-Supplement), 16-26. https://doi.org/10.33773/jum.1333260
AMA Nacaroğlu Y. ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS. JUM. October 2023;6(3-Supplement):16-26. doi:10.33773/jum.1333260
Chicago Nacaroğlu, Yaşar. “ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS”. Journal of Universal Mathematics 6, no. 3-Supplement (October 2023): 16-26. https://doi.org/10.33773/jum.1333260.
EndNote Nacaroğlu Y (October 1, 2023) ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS. Journal of Universal Mathematics 6 3-Supplement 16–26.
IEEE Y. Nacaroğlu, “ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS”, JUM, vol. 6, no. 3-Supplement, pp. 16–26, 2023, doi: 10.33773/jum.1333260.
ISNAD Nacaroğlu, Yaşar. “ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS”. Journal of Universal Mathematics 6/3-Supplement (October 2023), 16-26. https://doi.org/10.33773/jum.1333260.
JAMA Nacaroğlu Y. ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS. JUM. 2023;6:16–26.
MLA Nacaroğlu, Yaşar. “ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS”. Journal of Universal Mathematics, vol. 6, no. 3-Supplement, 2023, pp. 16-26, doi:10.33773/jum.1333260.
Vancouver Nacaroğlu Y. ON LEAP ZAGREB INDICES OF A SPECIAL GRAPH OBTAINED BY SEMIGROUPS. JUM. 2023;6(3-Supplement):16-2.