ANALYZING FUZZY MATRICES AND CONNECTIVITY IN SPECTRAL FUZZY GRAPH THEORY

Senbaga Priya K.; Buvaneswari R.

doi:10.29121/shodhkosh.v5.i6.2024.4301

Authors

K. Senbaga Priya Research Scholar, Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore, Tamil Nadu, India.
R. Buvaneswari Assistant Professor, Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore, Tamil Nadu, India.

DOI:

https://doi.org/10.29121/shodhkosh.v5.i6.2024.4301

Keywords:

Adjacency Eigenvalue, Laplacian Eigenvalue, Fuzzy Vertex Connectivity, Second Smallest Laplacian Eigenvalue, Maximum Strong Degree

Abstract [English]

In this paper, an analysis is conducted on several fuzzy matrices associated with a fuzzy graph, including the adjacency matrix A(G) and the Laplacian matrix L(G). The eigenvalues of the adjacency matrix (λi) of a fuzzy graph and their properties are stated and discussed. Fuzzy vertex connectivity (κ), along with algebraic connectivity (ϑn−1), adjacency, and Laplacian eigenvalues, are studied under
conditions κ ≤ q to make contributions to spectral fuzzy graph theory, enhancing the connectivity in network structures due to the occurrence of linguistic and inexact variables. Additionally, the relation- ship between κ and ϑn−1 shows the strength of connectivity among the vertices.

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