𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Minimizing a class of unicyclic graphs by means of Hosoya index

✍ Scribed by Hongbo Hua

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
481 KB
Volume
48
Category
Article
ISSN
0895-7177

No coin nor oath required. For personal study only.

✦ Synopsis

The Hosoya index, denoted by z(G), of a (molecular) graph G is defined as the total number of independent-edge sets of G. Let U n be the set of unicyclic graphs with n vertices. A fully loaded unicyclic graph is a unicyclic graph with the property that there is no vertex with degree less than 3 in its unique cycle. Denote by U 1 n the set of fully loaded unicyclic graphs. In this paper, graphs in U 1 n with minimal, second-minimal and third-minimal Hosoya indices are uniquely determined, respectively.

πŸ“œ SIMILAR VOLUMES

Minimality considerations for graph ener
Minimality considerations for graph energy over a class of graphs
✍ Dongdong Wang; Hongbo Hua πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 649 KB

Let G be a graph on n vertices, and let CHP(G; Ξ») be the characteristic polynomial of its adjacency matrix A(G). All n roots of CHP(G; Ξ»), denoted by Ξ» i (i = 1, 2, . . . n), are called to be its eigenvalues. The energy E(G) of a graph G, is the sum of absolute values of all eigenvalues, namely, E(G

Minimizer graphs for a class of extremal
Minimizer graphs for a class of extremal problems
✍ Dan Ismailescu; Dan Stefanica πŸ“‚ Article πŸ“… 2002 πŸ› John Wiley and Sons 🌐 English βš– 93 KB πŸ‘ 2 views

## Abstract We consider the family of graphs with a fixed number of vertices and edges. Among all these graphs, we are looking for those minimizing the sum of the square roots of the vertex degrees. We prove that there is a unique such graph, which consists of the largest possible complete subgraph

On the Hosoya index and the Merrifield–S
On the Hosoya index and the Merrifield–Simmons index of graphs with a given clique number
✍ Kexiang Xu πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 377 KB

The Hosoya index and the Merrifield-Simmons index of a graph are defined as the total number of the matchings (including the empty edge set) and the total number of the independent vertex sets (including the empty vertex set) of the graph, respectively. Let W n,k be the set of connected graphs with

Minimal graphs of a torus, a projective
Minimal graphs of a torus, a projective plane and spheres and some properties of minimal graphs of homotopy classes
✍ Alexander V. Ivashchenko; Yeong-Nan Yeh πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 397 KB

## Contractible transformations of graphs consist of contractible gluing and deleting of vertices and edges of graphs. They partition all graphs into the family of homotopy classes. Contractible transformations do not change the Euler characteristic and the homology groups of graphs. In this paper