UNDERSTANDING THE MATHEMATICAL GRAPH THEORY WITH SPECIAL REFERENCE TO DOMINATION THEORY

Mallikarjun S Biradar

doi:10.29121/shodhkosh.v5.i5.2024.2862

Authors

Mallikarjun S Biradar Dept. of Mathematics, Govt. First Grade College, Chittapur-585211

DOI:

https://doi.org/10.29121/shodhkosh.v5.i5.2024.2862

Abstract [English]

Graph theory is a pivotal branch of mathematics with extensive applications across various disciplines, including computer science, biology, social sciences, and more. This paper delves into the intricacies of mathematical graph theory, emphasizing its fundamental concepts, properties, and theorems. Special attention is given to domination theory, a significant subfield within graph theory.

This theory has practical implications in network design, resource allocation, and social network analysis, providing efficient solutions for optimization problems. Researcher discussed various types of domination, including total domination, connected domination, and independent domination, each adding layers of complexity and applicability. The paper reviews critical results, key algorithms, and significant applications of domination theory. Through this comprehensive exploration, we aim to enhance the understanding of graph theory's role in solving complex real-world problems, highlighting the importance and versatility of domination concepts in mathematical and applied contexts.

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