Spectral Graph Theory: Eigen Values Laplacians and Graph Connectivity

Authors

  • J. Satish Kumar Department of Science and Humanities (Mathematics), Dhaanish Ahmed Institute of Technology, India
  • B. Archana Department of Science and Humanities (Chemistry), Faculty of Engineering, Karpagam Academy of Higher Education, India
  • K. Muralidharan, R. Srija Department of Science and Humanities (Mathematics), Dhaanish Ahmed Institute of Technology, India

DOI:

https://doi.org/10.63278/1321

Keywords:

Spectral graph theory, eigenvalues, Laplacian matrix, graph connectivity, adjacency matrix, algebraic connectivity.

Abstract

Spectral graph theory investigates how graph structures and specific matrix eigenvalues of adjacency matrices and Laplacian matrices relate to each other. The following paper explains fundamental spectral graph theory concepts by analyzing eigenvalues alongside Laplacians which help evaluate graph connectivity. The spectral characteristics of these matrices provide crucial insights into the graph structure that include properties regarding connectivity as well as expansion features and operational reliability. The paper explains essential theorems alongside applications and methodology of spectral analysis.

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How to Cite

J. Satish Kumar, B. Archana, and K. Muralidharan, R. Srija. 2025. “Spectral Graph Theory: Eigen Values Laplacians and Graph Connectivity”. Metallurgical and Materials Engineering 31 (3):78-84. https://doi.org/10.63278/1321.

Issue

Vol. 31 No. 3 (2025)

Section

Research

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Copyright (c) 2025 J. Satish Kumar, B. Archana, K. Muralidharan, R. Srija

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