ELLIPTIC CURVES OBTAINED FROM BIPARTITE KNESER B TYPE-k GRAPHS

被引：0

作者：

Sreekumar, K. G. ^{[1
]}

Singh, G. Suresh ^{[1
]}

Preenu, C. S. ^{[2
]}

机构：

[1] Univ Kerala, Dept Math, Thiruvananthapuram, India

[2] Univ Coll, Dept Math, Thiruvananthapuram, India

来源：

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS | 2023年 / 13卷

关键词：

elliptic curves; rank; Hosoya polynomials; j-invariant; bipartite B type-1 graphs;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to introduce a new family of elliptic curves from the Hosoya polynomials of a family of graphs namely bipartite Kneser B type -k graphs. The Hosoya polynomials for the bipartite Kneser B type -k graphs were first established, and then the family of elliptic curves was formed by using the Hosoya polynomials. It was observed that for many values of n, these elliptic curves have ranks one or zero. We derived a formula for calculating the elliptic curve's j - invariant and discovered that it is only dependent on the distance parameters of the bipartite B type-1 graphs. The bipartite B type-1 graphs are isomorphic to the SM balancing graph.

引用

页码：102 / 111

页数：10

共 14 条

[1] ANTONIEWICZ A., 2005, Universitatis Iagellonicae Acta Mathematica, V43, P21
[2] Relationship between the Hosoya polynomial and the hyper-Wiener index
Cash, GG
[J]. APPLIED MATHEMATICS LETTERS, 2002, 15 (07) : 893 - 895
[3] Izadi F, 2014, EUR J PURE APPL MATH, V7, P131
[4] ELLIPTIC CURVES ARISING FROM BRAHMAGUPTA QUADRILATERALS
Izadi, Farzali
Khoshnam, Foad
Moody, Dustin
Zargar, Arman Shamsi
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2014, 90 (01) : 47 - 56
[5] The state of elliptic curve cryptography
Koblitz, N
Menezes, A
Vanstone, S
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2000, 19 (2-3) : 173 - 193
[6] ON COMPACT ANALYTIC SURFACES .3
KODAIRA, K
[J]. ANNALS OF MATHEMATICS, 1963, 78 (01) : 1 - &
[7] Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one
Miller, Robert L.
[J]. LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2011, 14 : 327 - 350
[8] Ncambalala T, 2021, TWMS J APPL ENG MATH, V11, P724
[9] On the roots of Hosoya polynomial
Shyama, M. P.
Kumar, V. Anil
[J]. JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2016, 19 (01) : 199 - 219
[10] Automorphism groups of bipartite Kneser type-k graphs
Sreekumar, K. G.
Ramesh Kumar, P.
Manilal, K.
[J]. ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2023, 16 (03)

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