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Beyond the Vertex: A Contemporary Review of Graph Theory

by Sridhar
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 187 - Number 77
Year of Publication: 2026
Authors: Sridhar
10.5120/ijca2026926216

Sridhar . Beyond the Vertex: A Contemporary Review of Graph Theory. International Journal of Computer Applications. 187, 77 ( Jan 2026), 23-27. DOI=10.5120/ijca2026926216

@article{ 10.5120/ijca2026926216,
author = { Sridhar },
title = { Beyond the Vertex: A Contemporary Review of Graph Theory },
journal = { International Journal of Computer Applications },
issue_date = { Jan 2026 },
volume = { 187 },
number = { 77 },
month = { Jan },
year = { 2026 },
issn = { 0975-8887 },
pages = { 23-27 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume187/number77/beyond-the-vertex-a-contemporary-review-of-graph-theory/ },
doi = { 10.5120/ijca2026926216 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2026-02-01T00:33:39.933072+05:30
%A Sridhar
%T Beyond the Vertex: A Contemporary Review of Graph Theory
%J International Journal of Computer Applications
%@ 0975-8887
%V 187
%N 77
%P 23-27
%D 2026
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Graph Theory, one of the most dynamic branches of discrete mathematics, provides a universal framework for modelling and analyzing systems defined by relationships and connectivity. Originating from Euler’s 1736 study of the Königsberg Bridge Problem, graph theory has evolved into a cornerstone of modern science and technology. This paper presents a comprehensive exploration of graph-theoretic concepts, including graph classifications, connectivity, trees, cycles, planarity, and directed graphs, highlighting their structural and computational significance. The study further examines the diverse applications of graph theory across computer science, engineering, biology, chemistry, social sciences, and operations research, emphasizing its role in data representation, optimization, and network modelling. With the increasing complexity of real-world systems, graphs serve as indispensable tools in areas such as artificial intelligence, big data analytics, cybersecurity, and quantum computing. Finally, the paper outlines emerging challenges—scalability in massive networks, temporal graph analysis, and the integration of graph learning within machine intelligence—that define the frontier of future research. By connecting classical principles with modern technological needs, this work underscores graph theory’s enduring relevance as a mathematical language of connectivity and complexity in the age of data and intelligence.

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Index Terms

Computer Science
Information Sciences

Keywords

Vertex Graph Coloring Bipartite

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