A study of dominating set for diamond graph using S polynomials

A system of polynomial equations which are used to model the dominating set problem in graph theory is given in [1]. In this article we compute the S-polynomials associated with the computation of Grobner basis for diamond graph with their Cartesian products and compute the varieties associated with...

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Bibliographic Details
Main Authors: Rajkumar, V., Sivakumar, B.
Format: Conference Proceeding
Language:English
Subjects:
Combinatorial analysis
Computation
Diamonds
Graph theory
Polynomials
Rings (mathematics)
Online Access:Get full text
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Summary:A system of polynomial equations which are used to model the dominating set problem in graph theory is given in [1]. In this article we compute the S-polynomials associated with the computation of Grobner basis for diamond graph with their Cartesian products and compute the varieties associated with the S-polynomials which in turn lead us to special sub graphs of the diamond graph. Through this we can show that there is a graph theoretic significance to the intermediate polynomials. We believe that this will be an answer for the question raised regarding the intermediate polynomials that occur during the actual computation of the universal Grobner basis given that both the initial ideal representation and the final universal Grobner basis have known combinatorial interpretations.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0164496