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A Method for Computing the Merrifield–Simmons Index on Benzenoid Systems
MATCH - Communications in Mathematical and in Computer Chemistry, 2022We present a method for computing the Merrifield-Simmons index on some basic graphs. For example, our proposal works on paths, simple cycles, trees, and we show that the method can be extended to process benzenoid systems Hr,t with a total of r.t hexagons.
De Ita, Guillermo +2 more
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Extremal Topologies for the Merrifield-Simmons Index on Dynamic Trees
2021In this article, we study the recognition of extremal topologies for the Merrifield-Simmons index in the space of tree graphs. We analyze how to obtain the maximum and the minimum number of independent set on these topologies when a new vertex v is joined to a tree \(T_n\) via a new edge \(\{v_p,v\}\), with \(v_p \in V(T_n)\) and \(v \notin V(T_n)\).
Pedro Bello 0001 +2 more
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On Merrifield-Simmons Index of Trees
2020Classification of graphs with respect to a parameter is an important optimization problem in graph theory. The Merrifield-Simmons index is defined as the total number of independent sets. This index can be calculated by recurrence relation in terms of Fibonacci numbers.
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Extending Extremal Polygonal Arrays for the Merrifield-Simmons Index
2017Polygonal array graphs have been widely investigated, and they represent a relevant area of interest in mathematical chemistry because they have been used to study intrinsic properties of molecular graphs. For example, to determine the Merrifield-Simmons index of a polygonal array \(A_n\) that is the number of independent sets of that graph, denoted as
Guillermo De Ita Luna +4 more
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The Hosoya Index and the Merrifield–Simmons Index of Some Nanostructures
2016The Hosoya index and the Merrifield–Simmons index are two types of graph invariants used in mathematical chemistry. In this chapter, we give ex act formulas for the Hosoya index and the Merrifield–Simmons index of bridge graph and as an application of these formulas, we obtain these indices for some nano structures.
Asma Hamzeh +3 more
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Minimal Merrifield-Simmons Index of 5-leaf-trees
2009 International Conference on Computational Intelligence and Security, 2009A tree T is called a r-leaf-tree if T has r pendent vertices. In this paper, we characterized trees with the second and third minimal Merrifield-Simmons index in the set of 5-leaf-trees of order n.
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On Hosoya Index and Merrifield‐Simmons Index of trees with given domination number
Numerical Methods for Partial Differential Equations, 2020AbstractThe Hosoya index and the Merrifield‐Simmons index are two important molecular descriptors in chemical graph theory. The Hosoya index is defined as the total number of matchings of the graph and the Merrifield‐Simmons index is defined as the total number of independent sets of the graph.
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The Merrifield-Simmons Index of Some Lexicographic Product Graphs
2016 8th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC), 2016Using the structure characteristics of join graph and lexicographic product, researching into the Merrifield-Simmons index for lexicographic product constructed path, cycle and other special graphs with arbitrarily graph, this essay therefore comes at the counting expression and arrangement results of the Merrifield-Simmons index.
Shuangliang Tian +3 more
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The Merrifield-Simmons index for two types of phenylenes
2020The Merrifield-Simmons index i(G) of a simple undirected graph G=(V,E) is the number of all independent sets of vertices in G. This number is one of the most popular topological indices in chemistry. In this contribution we obtain exact formulas for the Merrifield-Simmons index of two types of the branched phenylenes whose molecular graph consists of ...
Seibert, Jaroslav, Koudela, Libor
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The Merrifield-Simmons index for the linear octagonal chains
2019The Merrifield-Simmons index for a simple undirected graph G=(V,E) is given by the number of subsets U of V such that no two vertices in U are adjacent. This number is one of the most popular topological index in chemistry, which was firstly defined and called as the Fibonacci number of a graph.
Seibert, Jaroslav, Zahrádka, Jaromír
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