Algorithmic releases on the spanning trees of suitable graphs

TL;DR

This paper introduces a novel algebraic and combinatorial method to compute the number and structure of spanning trees in certain graphs, independent of Laplacian spectrum, with applications in secure communication.

Contribution

It presents an original, spectrum-independent algorithm for identifying all spanning trees in Jahangir graphs, including source code and security applications.

Findings

Developed an alternative method to compute spanning trees without Laplacian spectrum

Provided algorithm and source code for Jahangir graphs

Applied the method to enhance security in confidential information transmission

Abstract

In this paper algebraic and combinatorial properties and a computation of the number of the spanning trees are developed for certain graphs. To this purpose, an original method, independent of the spectrum of the Laplacian matrix associated to the graph, is discussed. It represents an alternative process to compute how many and which are the spanning trees of any graph and substantially consists in joining the spanning trees on the ground of the number of common edges between the inner cycles of it. The algorithm and its source code for determining the collection of all edge-sets of the spanning trees for the class of Jahangir graphs are displayed. An application involving such graphs in order to get a satisfactory degree of security in transmitting confidential information is given, and finally symmetry properties of them are highlighted.