# Spectral Graph Theory, Molecular Graph Theory and Their Applications

A special issue of *Axioms* (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".

Deadline for manuscript submissions: **closed (30 June 2024)** | Viewed by 9238

## Special Issue Editor

**Interests:**spectral graph theory; extrema lGraph theory; molecular graph theory; graph labeling; graph algorithm; discrete mathematics; combinatorics

Special Issues, Collections and Topics in MDPI journals

## Special Issue Information

Dear Colleagues,

Graph Theory is the area of mathematics that studies networks or graphs. It arose from the need to analyze many diverse network-like structures like the internet, molecules, road networks, social networks, education networks, and electrical networks. Spectral graph theory (a branch of graph theory) deals with the connection between the eigenvalues of a matrix associated with a graph and the corresponding structure of the graph. The first practical need for studying graph eigenvalues was in quantum chemistry in the nineteen-thirties, forties, and fifties, specifically to describe the Hückel molecular orbital theory for unsaturated conjugated hydrocarbons. Several special kinds of graph matrices (adjacency matrix, Laplacian matrix, signless Laplacian matrix, distance matrix, etc.) are very popular in spectral graph theory.

A graphical invariant is a function from the set of graphs to the set of reals which is invariant under graph automorphisms. In chemical graph theory, graphical invariants are most often referred to as topological indices. Among the oldest and most well-known topological indices, Wiener index, Randić index, and Zagreb indices, etc. were introduced in the literature. In the last twenty years, a large number of mathematical investigations were reported on graph invariants (topological indices) whose origin is in chemistry, and which are claimed to have chemical applications.

The aim of this Special Issue is to publish original research articles focusing on spectral graph theory and the topological indices of graphs, as well as applications in these areas. To find new connections between the eigenvalues and eigenvectors of graphs and graph theory, parameters such as average degree, maximum degree, cliques, chromatic number, and matching number are welcome. In addition, this Special Issue covers the characterization of extremal graphs with respect to the existing popular topological indices of graphs with fixed graph parameters.

Prof. Dr. Kinkar Chandra Das*Guest Editor*

**Manuscript Submission Information**

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## Keywords

- spectral graph theory
- topological indices of graphs
- energy of graphs
- combinatorics
- extremal graph theory
- graph polynomials