Characteristics of Soft Semitrees: Enhancing the Soft Semigraph Framework

Authors

  • Bobin George Pavanatma College Murickassery
  • Rajesh K. Thumbakara Mar Athanasius College (Autonomous) Kothamangalam
  • Sijo P. George Pavanatma College Murickassery
  • Jinta Jose Viswajyothi College of Engineering and Technology Vazhakulam

Keywords:

Soft Set, Semigraph, Soft Semigraph, Soft Semitree

Abstract

Molodtsov pioneered the concept of soft sets, offering a method to classify elements of a universe based on a specified set of parameters. This approach serves to model vagueness and uncertainty. Semigraphs are a generalized form of graphs introduced by Sampathkumar. The integration of soft set theory into semigraphs led to the creation of soft semigraphs. Due to its adeptness in handling parameterization, the field of soft semigraph theory is rapidly evolving. In this study, we introduce the concept of soft semitrees and explore some of their characteristics.

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References

M. Akram and S. Nawaz, Operations on Soft Graphs, Fuzzy Inf. Eng. 7(2015) 423-

, doi:10.1016/j. ae.2015.11.003.

M. Akram and S. Nawaz, Certain Types of Soft Graphs, U. P. B. Sci. Bull., Se-

ries A 78(4)(2016) 67-82, https://www.scientificbulletin.upb.ro/rev_docs_

arhiva/fullcc2_842873.pdf.

M. Akram and S. Nawaz, On fuzzy soft graphs, Italian Journal of Pure and Ap-

plied Mathematics 34(2015) 463-480, https://ijpam.uniud.it/online_issue/

/44-AkramNawaz.pdf.

M. Akram and S. Nawaz, Fuzzy soft graphs with applications, Journal of Intelligent

and Fuzzy Systems 30(6)(2016) 3619-3632, doi:10.3233/IFS-162107.

M. Akram and G. Shahzadi, Decision-making approach based on

Pythagorean Dombi fuzzy soft graphs, Granular Computing 6 (2021) 671-689,

doi:10.3390/mca24040102.

M. Akram and F. Zafar, On soft trees, Buletinul Acad. Stiinte a Republicia Moldova.

Mathematica 2(78)(2015) 82{95, https://www.math.md/files/basm/y2015-n2/

y2015-n2-(pp82-95).pdf.

M. Akram and F. Zafar, Fuzzy soft trees, Southeast Asian Bulletin of

Mathematics 40(2)(2016) 151-170, http://www.seams-bull-math.ynu.edu.cn/

downloadfile.jsp?filemenu=_201602&filename=01_40(2).pdf.

B. George, J. Jose, and R. K. Thumbakara, An Introduction to Soft Hypergraphs,

Journal of Prime Research in Mathematics 18(2022) 43-59, https://jprm.sms.

edu.pk/an-introduction-to-soft-hypergraphs/.

B. George, J. Jose, and R. K. Thumbakara, Modular Product of Soft

Directed Graphs, TWMS Journal of Applied and Engineering Mathematics

(3) (2024) 966-980, https://jaem.isikun.edu.tr/web/index.php/current/

-vol14no3/1229-modular-product-of-soft-directed-graphs.

B. George, J. Jose, and R. K. Thumbakara, Tensor Products and Strong Products

of Soft Graphs, Discrete Mathematics, Algorithms and Applications 15(8) (2023)

-28, doi:10.1142/S1793830922501713.

B. George, J. Jose, and R. K. Thumbakara, Co-normal Products and Modular

Products of Soft Graphs, Discrete Mathematics, Algorithms and Applications 16

(2) (2024), 1-31, doi:10.1142/S179383092350012X

B. George, R. K. Thumbakara, and J. Jose, Soft Semigraphs and Some of Their

Operations, New Mathematics and Natural Computation 19 (2) (2023) 369-385,

doi:10.1142/S1793005723500126.

B. George, R. K. Thumbakara, and J. Jose, Soft Semigraphs and Di erent Types

of Degrees, Graphs and Matrices Associated with Them, Thai Journal of Mathe-

matics 21 (4) (2023), 863-886, https://thaijmath2.in.cmu.ac.th/index.php/

thaijmath/article/view/1551.

B. George, J. Jose, and R. K. Thumbakara, Exploring Soft Hypergraphs Through

Various Operations, New Mathematics and Natural Computation (2023)(Published

Online), doi:10.1142/S1793005724500303.

B. George, J. Jose, and R. K. Thumbakara, Connectedness in Soft Semigraphs,

New Mathematics and Natural Computation 20 (1) (2024), 157-182, 10.1142/

S1793005724500108.

B. George, J. Jose, and R. K. Thumbakara, Investigating the Traits of

Soft Semigraph-Associated Degrees, New Mathematics and Natural Computa-

tion(2023)(Published Online), doi:10.1142/S1793005724500352.

B. George, J. Jose, and R. K. Thumbakara, Cartesian Product and Composition

of Soft Semigraphs, New Mathematics and Natural Computation (2023) (Published

Online), doi:10.1142/S1793005725500036.

B. George, J. Jose, and R. K. Thumbakara, Soft Semigraph Isomorphisms:

Classi cation and Characteristics, New Mathematics and Natural Computa-

tion(2023)(Published Online), doi:10.1142/S1793005725500255.

B. George, J. Jose, and R. K. Thumbakara, Eulerian and Hamiltonian Soft Semi-

graph, International Journal of Foundations of Computer Science (2024) (Published

Online), doi:10.1142/S0129054124500138.

B. George, J. Jose, and R. K. Thumbakara, Understanding Bipartite Soft Semigraph

Structures, Italian Journal of Pure and Applied Mathematics (2024) (To Appear).

B. George, R. K. Thumbakara, and J. Jose, Soft Directed Hy-

pergraphs and Their AND & OR Operations, Mathematical Fo-

rum (2022)(Published Online), https://mathematical-forum.org/

soft-directed-hypergraphs-and-their-and-or-operations/.

B. George, J. Jose, and R. K. Thumbakara, Soft Disemigraphs, Degrees and Di-

graphs Associated and Their AND & OR Operations, New Mathematics and Nat-

ural Computation (2023) (Published Online), doi:10.1142/S1793005723500448.

J. Jose, B. George, and R. K. Thumbakara, Soft Directed Graphs, Their Ver-

tex Degrees, Associated Matrices and Some Product Operations, New Mathemat-

ics and Natural Computation 19 (3) (2023), 651-686, https://doi.org/10.1142/

S179300572350028X.

J. Jose, B. George, and R. K. Thumbakara, Homomorphic Product of Soft Directed

Graphs, TWMS Journal of Applied and Engineering Mathematics (2022) (To Ap-

pear).

J. Jose, B. George, and R. K. Thumbakara, Soft Directed Graphs, Some of Their

Operations, and Properties, New Mathematics and Natural Computation 20 (1)

(2024), 129-155, doi:10.1142/S1793005724500091.

J. Jose, B. George, and R. K. Thumbakara, Rooted Product and Restricted Rooted

Product of Soft Directed Graphs, New Mathematics and Natural Computation

(2023) (Published Online), doi:10.1142/S1793005724500194.

J. Jose, B. George, and R. K. Thumbakara, Corona Product of Soft Directed

Graphs, New Mathematics and Natural Computation (2023) (Published Online),

doi:10.1142/S179300572550022X.

J. Jose, B. George, and R. K. Thumbakara, Disjunctive Product of Soft Directed

Graphs, New Mathematics and Natural Computation (2023)(Published Online),

doi:10.1142/S1793005725500139.

J. Jose, B. George, and R. K. Thumbakara, Eulerian and Unicursal Soft

Graphs, Mapana Journal of Sciences 22 (4) (2023), 99-113, https://journals.

christuniversity.in/index.php/mapana/article/view/4144.

P. K. Maji and A. R. Roy, A fuzzy soft set theoretic approach to decision-making

problems, Journal of Computational and Applied Mathematics 203 (2007), 412-418,

doi:10.1016/j.cam.2006.04.008.

P. K. Maji, A. R. Roy, and R. Biswas, An Application of Soft Sets in a Decision

Making Problem, Computers and Mathematics with Application 44 (2002) 1077-

, doi:10.1016/S0898-1221(02)00216-X.

D. Molodtsov, Soft Set Theory-First Results, Computers & Mathematics with Ap-

plications 37(1999) 19-31, doi:10.1016/S0898-1221(99)00056-5.

H. S. Nawaz and M. Akram, Oligopolistic Competition Among the Wireless In-

ternet Service Providers of Malaysia Using Fuzzy Soft Graphs, Journal of Applied

Mathematics and Computing 67(2021) 855-890, doi:10.1007/s12190-021-01514-z.

S. Saleh, T. M. Al-Shami, L. R. Flaih, M. Arar, and R. Abu-Gdairi, Ri-Separation

axioms via Supra Soft Topological Spaces, J. Math. Compt. Sci. 32 (2024), 263-274,

doi:10.22436/jmcs.032.03.07.

S. Saleh, L. R. Flaih, and K. F. Jasim, Some Applications of Soft -closed Sets

in Soft Closure Space, Communications in Mathematics and Applications, 14

(2) (2023), 481-492, https://www.researchgate.net/publication/373629819_

Some_applications_of_soft_-closed_sets_in_soft_closure_spaces.

E. Sampathkumar, Semigraph and their Applications, Technical Report (DST/MS/

/94), Department of Science and Technology, Govt. of India (1999).

E. Sampathkumar, C. M. Deshpande, B. Y. Yam, L. Pushpalatha, and V. Swami-

nathan Semigraph and Their Applications (Academy of Discrete Mathematics and

Applications, 2019).

J. D. Thenge, B. S. Reddy, and R. S. Jain, Connected Soft Graph, New Mathematics

and Natural Computation 16(2)(2020) 305-318, doi:10.1142/S1793005720500180.

J. D. Thenge, B. S. Reddy, and R. S. Jain, Contribution to Soft Graph and

Soft Tree, New Mathematics and Natural Computation 15(1)(2019) 129-143,

doi:10.1142/S179300571950008X.

J. D. Thenge, B. S. Reddy, and R. S. Jain, Adjacency and Incidence Matrix of a

Soft Graph, Communications in Mathematics and Applications 11 (1) (2020) 23-30,

doi:10.26713/cma.v11i1.1281.

R. K. Thumbakara and B. George, Soft Graphs, Gen. Math. Notes 21(2)(2014) 75-

, http://emis.icm.edu.pl/journals/GMN/yahoo_site_admin/assets/docs/

_GMN-4802-V21N2.16902935.pdf.

R. K. Thumbakara, B. George, and J. Jose, Subdivision Graph, Power and

Line Graph of a Soft Graphs, Communications in Mathematics and Applications

(1)(2022) 75-85, doi:10.26713/cma.v13i1.1669.

R. K. Thumbakara, J. Jose, and B. George, Hamiltonian soft graphs,

Ganita 72(1)(2022) 145-151, https://bharataganitaparisad.com/wp-content/

uploads/2022/11/721-ch15.pdf.

R. K. Thumbakara, J. Jose, and B. George, On Soft Graph Isomor-

phism, New Mathematics and Natural Computation (2023) (Published Online),

doi:10.1142/S1793005725500073.

Published

20-02-2025

How to Cite

Bobin George, Rajesh K. Thumbakara, Sijo P. George, & Jinta Jose. (2025). Characteristics of Soft Semitrees: Enhancing the Soft Semigraph Framework. Communications in Mathematics and Applications, 15(3). Retrieved from https://rgnpublications.com/journals/index.php/cma/article/view/2828

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Section

Research Article