B. Praba and M. Logeshwari.
Wiener Index of Rough Co-Zero Divisor Graph of a Rough Semiring
Dynamic Systems and Applications 30 (2021) No. 9, 1519 – 1544

https://doi.org/10.46719/dsa202130.09.08

ABSTRACT.
In this proposed article we consider an approximation space I=(U,R), where U denotes nonempty finite set of objects and R be an arbitrary equivalence relation defined on U. The Rough Co-zero divisor graph G(Z*(J)) of a Rough Semiring (T, ∆,∇) on I corresponding to the Rough ideal is taken for study. The degree of each of the vertices and distance of any two vertices in G(Z*(J)) are computed. Based on the degree of vertices a Partition graph P(Z*(J)) is defined. This Partition graph is used to find the Wiener index of G(Z*(J)). The main advantage of partition graph is that all the graph theoretical parameters can be computed for any Rough Co-zero divisor graph with 2^{n-m}.3^m – 2, 1 ≤ m ≤ n. An analysis of disease symptom relationship is made through the defined parameters. All of the concepts are embellished with suitable examples.

AMS Classification: 05C12, 05C05

Keywords: Degree, Distance, Rough Co-Zero Divisor Graph, Partition Graph, Wiener Index.