Graph Invariants and Their Applications

Dear Colleagues,

Graph theory plays a pivotal role in various branches of mathematics and its applications, particularly in chemical graph theory and algebraic graph theory. This Special Issue is dedicated to exploring the latest advancements in graph invariants and their diverse applications across discrete mathematics and related disciplines.

Chemical graph theory, a prominent area of mathematical chemistry, utilizes graph invariants to model and analyze chemical phenomena. One of its core concepts is that of topological indices—numerical graph invariants derived from the molecular graph representations of chemical compounds. These indices are invariant under graph isomorphisms and serve as critical tools in structure–property and structure–activity relationship studies. Since their inception in 1947, numerous indices have been introduced based on various graph-theoretic parameters, such as degree, distance, eccentricity, entropy, and spectral properties.

Alongside this, matrices and graphs offer complementary perspectives on discrete structures. While matrix representations can shed light on combinatorial properties, graphs associated with matrices provide meaningful insights into the matrices themselves. Spectral graph theory, which studies the eigenvalues (spectrum) of matrices associated with graphs, has emerged as a powerful analytical framework. It employs tools from linear algebra to explore structural and functional characteristics of graphs, including graph energy and other spectral properties.

This Special Issue invites high-quality contributions presenting novel findings in chemical and algebraic graph theory, with an emphasis on graph invariants and their mathematical and practical implications. We welcome papers that address both theoretical advancements and real-world applications.

Topics of interest include, but are not limited to, the following:

• Graph invariants;
• Topological indices;
• Graph spectrum and energy;
• Extremal graph theory;
• Graph coloring;
• QSPR/QSAR analysis;
• Combinatorics;
• Discrete mathematics.

We aim to collate cutting-edge research that highlights the depth and breadth of this vibrant area, offering new perspectives and tools for both theoretical exploration and applied science.

Prof. Dr. Kinkar Chandra Das
Guest Editor

Manuscript Submission Information

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• graph invariants
• topological indices
• graph spectrum and energy
• extremal graph theory
• graph coloring
• QSPR/QSAR analysis
• combinatorics
• discrete mathematics