LINE GRAPH ASSOCIATED WITH C-PRIME GRAPH OF A NEARRING
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper we introduce a line graph of c-prime graph of a near- ring N with respect to an ideal I denoted by L(CI (N)): We nd properties of this graph. We nd diameter, girth and obtain conditions for L(CI (N)) is a complete graph. We nd interrelation between L(GI (N)), L(CI (N)): We prove that near- ring homomorphism between two nearrings is a graph homomorphism between corresponding c-prime line graphs.
Abstract
In this paper we introduce a line graph of c-prime graph of a near- ring N with respect to an ideal I denoted by L(CI (N)): We nd properties of this graph. We nd diameter, girth and obtain conditions for L(CI (N)) is a complete graph. We nd interrelation between L(GI (N)), L(CI (N)): We prove that near- ring homomorphism between two nearrings is a graph homomorphism between corresponding c-prime line graphs.
참고문헌 (17)
- D. D. Anderson, "On total graph of a commutative ring", J. Algebra, 320, pp.2706~2719 (2008)
- D. D. Anderson, "The zero divisor graph of a commutative ring", J. Algebra, 217, pp.434~437 (1999)
- I. Beck, "Coloring of commutative rings", J. Algebra, 116, pp.208~226 (1998)
- S. Bhavanari, "Nearrings, fuzzy ideals and graph theory", pp.2013, Chapman and Hall
- S. Bhavanari, "Graph of a nearring with respect to an ideal", Commun. Algebra, 38, pp.1957~1962 (2010)
- G. L. Booth, "A Kurosh-Amitsur prime radical for near-rings", Commun. Algebra, 18(9), pp.3111~3122 (1990)
- T. T. Chelvam, "Zero divisor graph of an ideal of a nearring", Discrete Math. Algorithms and Appl, 5, pp.13500071~135000711 (2013)
- J. Clark, "A first look at Graph theory" (2001), World Scientific Press Ltd
- C. C. Ferrero, "Nearrings: Some developments Linked to Semigroups and Groups" (2002), Kluwer Acadamic Publishers
- F. Harary, "Graph theory" (2001), Naraosa Publishing House
- P. Hell, "Graphs and Homomorphisms" (2004), Oxford University press
- B. Jagadeesha, "Interval Valued L-fuzzy Ideals based on t-norms and t-conorms", Journal of Intelligent and Fuzzy System, 28(6), pp.2631~2641 (2015)
- B. S. Kedukodi, "Different prime graphs of a nearring with respect to an ideal", Nearrings, Nearfields and related topics, World Scientific, pp.185~203 (2017)
- S. P. Kuncham, "Interval valued L-fuzzy cosets and isomor-phism theorems", Afrika Matematika, 27, pp.393~408 (2016)
- G. Pilz, "Near-Rings" (1983), Revised edition
- M. Sarmah, "On zero-divisor graphs of small nite commutative rings", Tamkang J. Maths, 52, pp.341~347 (2021)
- S. P. Redmond, "Line Graph associated with graph of nearring", Discrete Math, 307, pp.1155~1166 (2007)
