Results 1 to 10 of about 78 (53)

The expected values of the total numbers of independent edge sets and independent sets in random alpha-type pentagonal chains [PDF]

Heliyon, 2023
A independent edge set of G containing mutually independent edges is also called a matching of G. The total numbers of matchings and independent sets of a graph G, namely, the Hosoya index and the Merrifield-Simmons index, respectively, are two important
Lina Wei, Hong Bian, Haizheng Yu
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The Expected Value of Hosoya Index and Merrifield–Simmons Index in a Random Cyclooctylene Chain

Axioms, 2022
The Hosoya index m(G) and the Merrifield–Simmons index i(G) of a graph G are the number of matchings and the number of independent sets in G. In this paper, we establish exact formulas for the expected value of the Hosoya index and Merrifield–Simmons ...
Yushuang Sun, Xianya Geng
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The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four

Journal of Mathematics, 2021
The Merrifield–Simmons index iG of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, i.e., the number of independent vertex sets of G.
Kun Zhao, Shangzhao Li, Shaojun Dai
doaj   +1 more source

On Merrifield-Simmons index of molecular graphs [PDF]

Kragujevac Journal of Science, 2016
The Merrifield-Simmons index σ = σ(G) of a graph G is the number of independent vertex sets of G. This index can be calculated recursively and expressed in terms of Fibonacci numbers.
Gutman Ivan, Gültekin Inci, Şahin Bünyamin   +2 more
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The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs

Journal of Applied Mathematics, 2012
The Merrifield-Simmons index i(G) of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets of G The Hosoya index z(G) of a graph G is defined as the ...
Shaojun Dai, Ruihai Zhang
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The Hosoya index and the Merrifield-Simmons index of some graphs [PDF]

Transactions on Combinatorics, 2012
The Hosoya index and the Merrifield-Simmons index are two types of graph invariants used in mathematical chemistry. In this paper, we give some formulas for computed these indices for some classes of corona product and link of two graphs. Furthermore, we
Samaneh Hossein-Zadeh, Mohammad Ali Hosseinzadeh, Ali Iranmanesh, Asma Hamzeh   +3 more
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Merrifield-Simmons Index in Random Phenylene Chains and Random Hexagon Chains

Discrete Dynamics in Nature and Society, 2015
The author obtains explicit expressions for the expected value of the Merrifield-Simmons index of a random phenylene chain and a random hexagon chain, respectively.
Ailian Chen
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Hosoya and Merrifield-Simmons indices of some classes of corona of two graphs [PDF]

Transactions on Combinatorics, 2012
Let G = (V;E) be a simple graph of order n and size m. An r-matching of G is a set of r edges of G which no two of them have common vertex. The Hosoya index Z(G) of a graph G is defined as the total number of its matchings.
Mohammad Ali Iranmanesh, Saeid Alikhani, Mohammad Hossein Reyhani   +2 more
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A Data-Driven Graph Neural Network Framework for Predicting Topological Indices of Unicyclic and Bicyclic Graphs

Algorithms
Topological indices provide numerical descriptions of graph structure and support graph analysis in cheminformatics, network design, and graph mining.
Nadia Khan, Muhammad Zeeshan, Yousaf Iqbal, Mansoor Iqbal, Muhammad Amjad Iqbal, Sheraz Aslam   +5 more
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Counting Rules for Computing the Number of Independent Sets of a Grid Graph

Mathematics
The issue of counting independent sets of a graph, G, represented as i(G), is a significant challenge within combinatorial mathematics. This problem finds practical applications across various fields, including mathematics, computer science, physics, and
Guillermo De Ita Luna, Pedro Bello López, Raymundo Marcial-Romero   +2 more
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