Abstract
In graph theory, the Kirchhoff index serves as a metric to evaluate the complexity of a graph. It is determined by adding up the resistance distances between every pair of vertices in the graph. In a network created from the given graph by substituting each edge by a unit resistor, the resistance distance between a pair of specified vertices is equivalent to the electrical resistance between them in the constructed network. Basically, it measures the convenience with which data or flow can move between various locations in a network that the graph represents. In terms of graph matrices, the Kirchhoff index of a graph is equal to the total of the inverses of the positive Laplacian eigenvalues of the graph. It has profound applications in chemical graph theory and as such it has been studied for several linear and cylinder chains of chemically important graphs. In this paper, the spiro para-hexagonal cylinder chain is considered and its Kirchhoff index, Wiener index and number of spanning trees are obtained. The ratio of the Wiener index and Kirchhoff index for large graphs of this class is also observed to approach 3, as found for many other chain graphs earlier.
Recommended Citation
Reja, Md Selim and Abu Nayeem, Sk. Md.
(2026).
(SI16 No07) Computing the Kirchhoff Index and the Wiener Index of Spiro Para Hexagonal Cylinder Chain,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 21,
Iss.
3, Article 1.
Available at:
https://digitalcommons.pvamu.edu/aam/vol21/iss3/1