A New prospect of Matroid Theory
Mr. Ajay Kumar
, Dr. Sushil Kumar Jamariar , Mr. Ratan Priye , Mr. Subodh Kumar Paswan
Graph theory, Linear Algebra, Bases, Rank Function , Circuite, Vertex-edge, Incidence Matrix.
A Matroid is a structure that generalizes the properties of independence . The name ‘Matroid ‘ suggests a structure related to a matrix and indeed , Matroids were introduced by Whiteney in 1938 to provide a unifying abstract treatment of dependence in linear algebra and graph theory ; Relevant applications are found in graph theory and linear Algebra. There are several ways to define a Matroid, each related to the concept of independence. A Characteristic of matroid is that they can be defined on many different be it equivalent ways . This paper will focus on the definitions of matrvids in terms of independent sets, bases, the rank function and cycles. This paper consists of preliminaries and each of the rest casists of a particular definition of Matroid and its application in graph theory and linear Algebra. Here we observe how both graphs and Matroids can be viewed as Matrices.
"A New prospect of Matroid Theory", IJSDR - International Journal of Scientific Development and Research (www.IJSDR.org), ISSN:2455-2631, Vol.9, Issue 3, page no.548 - 552, March-2024, Available :https://ijsdr.org/papers/IJSDR2403082.pdf
Volume 9
Issue 3,
March-2024
Pages : 548 - 552
Paper Reg. ID: IJSDR_210448
Published Paper Id: IJSDR2403082
Downloads: 000347321
Research Area: Mathematics
Country: Vaishali, Bihar, India
ISSN: 2455-2631 | IMPACT FACTOR: 9.15 Calculated By Google Scholar | ESTD YEAR: 2016
An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 9.15 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator
Publisher: IJSDR(IJ Publication) Janvi Wave
