scholarly journals Hosoya Index of Triangular and Alternate Triangular Snake Graphs

2020 ◽  
Vol 172 ◽  
pp. 240-246
Author(s):  
A. Shanthakumari ◽  
S. Deepalakshmi
Keyword(s):  
Hosoya Index

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

scholarly journals ON MAXIMAL ENERGY AND HOSOYA INDEX OF TREES WITHOUT PERFECT MATCHING

2009 ◽  
Vol 81 (1) ◽  
pp. 47-57 ◽  
Author(s):  
HONGBO HUA
Keyword(s):  
Maximal Element ◽  
Perfect Matching ◽  
Undirected Graph ◽  
Unique Element ◽  
Hosoya Index ◽  
Maximal Energy ◽  
Molecular Graphs ◽  
The Family ◽  
Appl Math ◽  
Chemical Trees

AbstractLet G be a simple undirected graph. The energy E(G) of G is the sum of the absolute values of the eigenvalues of the adjacent matrix of G, and the Hosoya index Z(G) of G is the total number of matchings in G. A tree is called a nonconjugated tree if it contains no perfect matching. Recently, Ou [‘Maximal Hosoya index and extremal acyclic molecular graphs without perfect matching’, Appl. Math. Lett.19 (2006), 652–656] determined the unique element which is maximal with respect to Z(G) among the family of nonconjugated n-vertex trees in the case of even n. In this paper, we provide a counterexample to Ou’s results. Then we determine the unique maximal element with respect to E(G) as well as Z(G) among the family of nonconjugated n-vertex trees for the case when n is even. As corollaries, we determine the maximal element with respect to E(G) as well as Z(G) among the family of nonconjugated chemical trees on n vertices, when n is even.

Sign in / Sign up

Export Citation Format

Share Document