Skip to main content
SpringerLink
Log in

Genus of graphs under picture fuzzy environment with applications

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

In this study, the embedding of picture fuzzy graphs on the surface of spheres is introduced. The picture fuzzy genus graph with its genus value and strong (weak) picture fuzzy genus graphs are defined. Some important properties of picture fuzzy genus graphs are discussed. A relation between genus value and degree of planarity of picture fuzzy graph is established. The isomorphism properties of picture fuzzy genus graphs are studied. The Euler polyhedral equation in terms of genus value is established here. Finally, two real-life applications of picture fuzzy genus graph in traffic problem on road network and electronic circuit design on planar sheet are exhibited.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Abdul-Jabbar N, Naoom JH, Ouda EH (2009) Fuzzy dual graph. J Al Nahrain Univ 12(4):168–171

    Google Scholar 

  • Agnarsson G, Greenlaw R (2008) Graph theory modeling, applications and algorithms. Pearson, Noida

    MATH  Google Scholar 

  • Akram M, Dar JM, Farooq A (2018) Planar graphs under pythagorean fuzzy environment. Mathematics 6:278. https://doi.org/10.3390/math6120278

    Article  MATH  Google Scholar 

  • Al-Hawary T, Mahamood T, Jan N, Ullah K, Hussain A (2018) On intuitionistic fuzzy graphs and some operations on picture fuzzy graphs. Ital J Pure Appl Math

  • Alshehri N, Akram M (2014) Intuitionistic fuzzy planar graphs. Discr Dyn Nat Soc. https://doi.org/10.1155/2014/397823

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  Google Scholar 

  • Bakbak D, Ulucay V (2019) Multicriteria decision-making method using the cosine vector similarity measure under intuitionistic trapezoidal fuzzy multi-numbers in architecture. In: 6th International Multidisciplinary Studies Congress (Multicongress’19) Gaziantep, Türkiye

  • Bakbak D, Ulucay V, Sahin M (2019) Intuitionistic trapezoidal fuzzy multi-numbers and some arithmetic averaging operators with their application in architecture. In: 6th International Multidisciplinary Studies Congress (Multicongress’19) Gaziantep, Türkiye

  • Balakrishnan VK (1997) Graph theory. McGraw-Hill, New York

    MATH  Google Scholar 

  • Conder M, Stokes K (2019) New methods for finding minimum genus embeddins of graphs on orientable and non-orientable surfaces. ARS Math Contemp 17:135

    Article  Google Scholar 

  • Cuong BC, Hai PV (2015) Some fuzzy logic operations for picture fuzzy sets. In: 7th International conference on knowledge and systems engineering, pp 132–137

  • Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420

    Google Scholar 

  • Das S, Ghorai G (2020) Analysis of road map design based on multigraph with picture fuzzy information. Int J Appl Comput Math 6(3):1–17

    Article  MathSciNet  Google Scholar 

  • Gross J, Klein E, Rieper R (1993) On the average genus of a graph. Graph Combin 9(2):153–162

    Article  MathSciNet  Google Scholar 

  • Harary F (1969) Graph theory. Addison Wesley Publishing Company, Boston

    Book  Google Scholar 

  • Kalathian S, Ramalingam S, Srinivasan N, Raman S, Broumi S (2020) Embedding of fuzzy graphs on topological surfaces. Neural Comput Appl 32(9):5059–5069

    Article  Google Scholar 

  • Kauffman A (1973) Introduction a la theorie des sousemsembles flous. Masson et cie editeurs, Paris, p 1

    Google Scholar 

  • Kavitha S, Kala R (2017) On the genus of graphs from commutative rings. AKCE Int J Graphs Combin 14(1):27–34

    Article  MathSciNet  Google Scholar 

  • Li Z, Ren H (2016) Minimum genus embeddings of the complete graph. Acta Math Sin 32(10):1246–1254

    Article  MathSciNet  Google Scholar 

  • Mandal S, Sahoo S, Ghorai G, Pal M (2018) Genus value of \(m\)-polar fuzzy graphs. J Intell Fuzzy Syst 34(3):1947–1957

    Article  Google Scholar 

  • Mohammadzadeh A, Kayacan E (2019) A non-singleton type-2 fuzzy neural network with adaptive secondary membership for high dimensional applications. Neurocomputing 338:63–71

    Article  Google Scholar 

  • Mohammadzadeh A, Kaynak O (2019) A novel general type-2 fuzzy controller for fractional-order multi-agent systems under unknown time-varying topology. J Franklin Inst 356(10):5151–5171

    Article  MathSciNet  Google Scholar 

  • Ok AO, Senaras C, Yuksel B (2012) Automated detection of arbitrarily shaped buildings in complex environments from monocular VHR optical satellite imagery. IEEE Trans Geosci Remote Sens 51(3):1701–1717

    Article  Google Scholar 

  • Pramanik T, Samanta S, Pal M (2014) Interval-valued fuzzy planar graphs. Int J Mach Learn Cyber 7(4):653–664

    Article  Google Scholar 

  • Rashmanlou H, Borzooei RA (2016) New concepts of interval-valued intuitionistic \((S, T)\)-fuzzy graphs. J Intell Fuzzy Syst 30(4):1893–1901

    Article  Google Scholar 

  • Rosenfeld A (1975) Fuzzy graphs. In: Zadeh LA, Fu KS, Shimura M (eds) Fuzzy sets and their applications. Academic Press, New York, pp 77–95

    Google Scholar 

  • Sahoo S, Ghorai G, Pal M (2018) Embedding and genus of intuitionistic fuzzy graphs on spheres. J Multi-Value Logic Soft Comput 31(1–2):139–154

    MathSciNet  MATH  Google Scholar 

  • Samanta S, Pal M (2015) Fuzzy planar graphs. IEEE Trans Fuzzy Syst 23(6):1936–1942

    Article  Google Scholar 

  • Shannon A, Atanassov KT (1994) A first step to a theory of the intuitionistic fuzzy graphs. In: Proceeding of FUBEST, pp 59–61

  • Son LH, Viet P, Hai P (2017) Picture inference system: a new fuzzy inference system on picture fuzzy set. Appl Intell 46(3):652–669

    Article  Google Scholar 

  • Thong PH, Son LH (2015) HIFCF: an effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis. Expert Syst Appl 42(7):3682–3701

    Article  Google Scholar 

  • Ulucay V, Deli I, Sahin M (2019) Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems. Complex Intell Syst 5(1):65–78

    Article  Google Scholar 

  • Yu W, Zhang Z, Zhong Q (2019) Consensus reaching for MAGDM with multi-granular hesitant fuzzy linguistic term sets: a minimum adjustment-based approach. Ann Oper Res. https://doi.org/10.1007/s10479-019-03432-7

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  • Zhang Z, Yu W, Martinez L, Gao Y (2019) Managing multigranular unbalanced hesitant fuzzy linguistic information in multiattribute large-scale group decision making: A linguistic distribution-based approach. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/tfuzz.2019.2949758

    Article  Google Scholar 

  • Zhang Z, Gao Y, Li Z (2020) Consensus reaching for social network group decision making by considering leadership and bounded confidence. Knowl-Based Syst. https://doi.org/10.1016/j.knosys.2020.106240

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102, India

    Sankar Das, Ganesh Ghorai & Madhumangal Pal

  2. Department of Mathematics, Kharagpur College, Kharagpur, 721 305, India

    Sankar Das

Authors
  1. Sankar Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ganesh Ghorai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Madhumangal Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ganesh Ghorai.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Table 3

Table 3 List of abbreviations
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, S., Ghorai, G. & Pal, M. Genus of graphs under picture fuzzy environment with applications. J Ambient Intell Human Comput 12, 10741–10756 (2021). https://doi.org/10.1007/s12652-020-02887-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-020-02887-y

Keywords

Search

Navigation