The Hosoya index and the Merrifield–Simmons index

Huang, Yufeng; Shi, Lei; Xu, Xingyu

doi:10.1007/s10910-018-0937-y

Cited by 10 publications

(8 citation statements)

References 14 publications

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“…Thus, a similar approach could be applied for computing the Hosoya index and the Hosoya matrix of tree-like graphs, e.g., cactus graphs, and of graphs derived from trees. Moreover, the presented concepts could initiate studies of efficient methods of computation for other topological indices, especially the ones that are closely connected to the Hosoya index, particularly the Merrifield-Simons index [17,18], the energy of a graph [3], and the matching energy of a graph [19].…”

Section: Discussionmentioning

confidence: 99%

Linear Algorithms for the Hosoya Index and Hosoya Matrix of a Tree

Vesel¹

2021

Mathematics

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The Hosoya index of a graph is defined as the total number of its independent edge sets. This index is an important example of topological indices, a molecular-graph based structure descriptor that is of significant interest in combinatorial chemistry. The Hosoya index inspires the introduction of a matrix associated with a molecular acyclic graph called the Hosoya matrix. We propose a simple linear-time algorithm, which does not require pre-processing, to compute the Hosoya index of an arbitrary tree. A similar approach allows us to show that the Hosoya matrix can be computed in constant time per entry of the matrix.

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Section: Discussionmentioning

confidence: 99%

Linear Algorithms for the Hosoya Index and Hosoya Matrix of a Tree

Vesel¹

2021

Mathematics

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“…Wang determined a class of unicyclic graphs and obtained the ordering of their Hosoya and Merrifield-Simmons indexes [139]. It turns out that graphs of minimal Hosoya index coincide with those of maximal Merrifield-Simmons index [125,140,141]. The absolute magnitudes of the coefficients of the HP and the matching polynomial of a caterpillar graph are identical to those of the sextet and resonance polynomials of a benzenoid system.…”

Section: Hosoya Polynomialmentioning

confidence: 99%

“…To further illustrate how this polynomial relates to chemistry, a starting point is the Merrifield-Simmons index-the number of independent vertex subsets of G, including ∅ [140,193]. Many properties of IP and HP are fully analogous.…”

Section: Independence Polynomialmentioning

confidence: 99%

Counting Polynomials in Chemistry: Past, Present, and Perspectives

Joița,

Tomescu,

Jäntschi

2023

Symmetry

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Counting polynomials find their way into chemical graph theory through quantum chemistry in two ways: as approximate solutions to the Schrödinger equation or by storing information in a mathematical form and trying to find a pattern in the roots of these expressions. Coefficients count how many times a property occurs, and exponents express the extent of the property. They help understand the origin of regularities in the chemistry of specific classes of compounds. Our objective is to accelerate the research of newcomers into chemical graph theory. One problem in understanding these concepts is in the different approaches and notations of each research study; some researchers provide online tools for computing these mathematical concepts, but these need to be maintained for functionality. We take advantage of similar mathematical aspects of 14 such polynomials that merge theoretical chemistry and pure mathematics; give examples, differences, and similarities; and relate them to recent research.

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“…S631-S638 [3]. They are defined as the total number of independent vertex subsets as in the following definition and consider the total number of matchings of a graph, see for details [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

On the Merrifield-Simmons index and generating functions for the graphs of the state PL(2,n)

Gultekin

Çevik

2022

THERM SCI

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In this study, we compute Merrifield-Simmons index of graphs which corresponds to PL (2, n) by using the decomposition formula. Examination shows that Merri-field-Simmons index of certain classes of graphs deduce as a result in a difference equation. Further, the prominent formula for Merrifield-Simmons index of PL (2, n) and generating function are found as a function of the number n of hexagons in the state of PL (2, n). Also the relations formed for the (PL (2, n, n)) graphs obtained by combining two PL (2, n) with a certain angle between them are given.

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The Hosoya index and the Merrifield–Simmons index

Cited by 10 publications

References 14 publications

Linear Algorithms for the Hosoya Index and Hosoya Matrix of a Tree

Linear Algorithms for the Hosoya Index and Hosoya Matrix of a Tree

Counting Polynomials in Chemistry: Past, Present, and Perspectives

On the Merrifield-Simmons index and generating functions for the graphs of the state PL(2,n)

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