scholarly journals Hosoya Index ofL-Type Polyphenyl Spiders

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Ren Shengzhang ◽  
Wu Tingzeng
Keyword(s):  
Hosoya Index ◽  
Independent Edge

The polyphenyl system is composed ofnhexagons obtained from two adjacent hexagons that are sticked by a path with two vertices. The Hosoya index of a graphGis defined as the total number of the independent edge sets ofG. In this paper, we give a computing formula of Hosoya index of a type of polyphenyl system. Furthermore, we characterize the extremal Hosoya index of the type of polyphenyl system.

scholarly journals The Merrifield-Simmons Index and Hosoya Index ofC(n,k,λ)Graphs

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Shaojun Dai ◽  
Ruihai Zhang
Keyword(s):  
Hosoya Index ◽  
Independent Vertex ◽  
Vertex Set ◽  
Independent Edge ◽  
Vertex Sets

The Merrifield-Simmons indexi(G)of a graphGis 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 ofGThe Hosoya indexz(G)of a graphGis defined as the total number of independent edge subsets, that is, the total number of its matchings. ByC(n,k,λ)we denote the set of graphs withnvertices,kcycles, the length of every cycle isλ, and all the edges not on the cycles are pendant edges which are attached to the same vertex. In this paper, we investigate the Merrifield-Simmons indexi(G)and the Hosoya indexz(G)for a graphGinC(n,k,λ).

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

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 142
Author(s):  
Aleksander Vesel
Keyword(s):  
Linear Time ◽  
Molecular Graph ◽  
Time Algorithm ◽  
Hosoya Index ◽  
Significant Interest ◽  
The Matrix ◽  
Independent Edge ◽  
Linear Algorithms ◽  
Arbitrary Tree ◽  
Structure Descriptor

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.

scholarly journals Two Classes of Topological Indices of Phenylene Molecule Graphs

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Tingzeng Wu
Keyword(s):  
Topological Indices ◽  
Extremal Graph ◽  
Hosoya Index ◽  
Matching Polynomial ◽  
Conjugated Hydrocarbons ◽  
Independent Edge ◽  
The Absolute

A phenylene is a conjugated hydrocarbons molecule composed of six- and four-membered rings. The matching energy of a graphGis equal to the sum of the absolute values of the zeros of the matching polynomial ofG, while the Hosoya index is defined as the total number of the independent edge sets ofG. In this paper, we determine the extremal graph with respect to the matching energy and Hosoya index for all phenylene chains.

scholarly journals A connection between the Kekulé structures of pentagonal chains and the Hosoya index of caterpillar trees

2017 ◽  
Vol 232 ◽  
pp. 230-234 ◽  
Author(s):  
Chuanqi Xiao ◽  
Haiyan Chen ◽  
Andrei M. Raigorodskii
Keyword(s):  
Hosoya Index ◽  
Kekulé Structures

THE HOSOYA INDEX OF GRAPHS FORMED BY A FRACTAL GRAPH

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950135 ◽  
Author(s):  
JIA-BAO LIU ◽  
JING ZHAO ◽  
JIE MIN ◽  
JINDE CAO
Keyword(s):  
Computational Complexity ◽  
Hosoya Index ◽  
Initial Graph ◽  
Np Complete

The computational complexity of the Hosoya index of a given graph is NP-Complete. Let [Formula: see text] be the graph constructed from [Formula: see text] by a triangle instead of all vertices of the initial graph [Formula: see text]. In this paper, we characterize the Hosoya index of the graph [Formula: see text]. To our surprise, it shows that the Hosoya index of [Formula: see text] is thoroughly given by the order and degrees of all the vertices of the initial graph [Formula: see text].

scholarly journals Extremal Chemical Trees

2002 ◽  
Vol 57 (1-2) ◽  
pp. 49-51
Author(s):  
Miranca Fischermann ◽  
Ivan Gutman ◽  
Arne Hoffmann ◽  
Dieter Rautenbach ◽  
Dušica Vidovića ◽  
...  
Keyword(s):  
Carbon Atom ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Wiener Index ◽  
Graph Representation ◽  
Hosoya Index ◽  
Saturated Hydrocarbons ◽  
Physico Chemical ◽  
Graph Energy ◽  
Chemical Trees

A variety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W. the largest graph eigenvalue λ1, the connectivity index X, the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W , λ1, E, and Z. whereas the analogous problem for X was solved earlier. Among chemical trees with 5. 6, 7, and 3k + 2 vertices, k = 2,3,..., one and the same tree has maximum λ1 and minimum W, E, Z. Among chemical trees with 3k and 3k +1 vertices, k = 3,4...., one tree has minimum 11 and maximum λ1 and another minimum E and Z .

Coulson function and Hosoya index

2002 ◽  
Vol 355 (3-4) ◽  
pp. 378-382 ◽  
Author(s):  
Ivan Gutman ◽  
Dušica Vidović ◽  
Boris Furtula
Keyword(s):  
Hosoya Index

The smallest Hosoya index in (n, n + 1)-graphs

2007 ◽  
Vol 43 (1) ◽  
pp. 119-133 ◽  
Author(s):  
Hanyuan Deng
Keyword(s):  
Hosoya Index
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