The Merrifield-Simmons index is related to several physicochemical characteristics and is thus of use in combinatorial chemistry, e.g. in drug design and molecular recognitions. In this paper, we show how one can algorithmically construct databases of acyclic molecular graphs with large Merrifield-Simmons index. Our algorithm can deal with a large number of atoms (several hundreds) in short tim...

We analyze the use, advantages, and drawbacks of graph kernels in chemoin-formatics, including a comparison of kernel-based approaches with other methodology, as well as examples of applications. Kernel-based machine learning [1], now widely applied in chemoinformatics, delivers state-of-the-art performance [2] in tasks like classification and regression. Molecular graph kernels [3] are a recen...

In a series of publications Estrada (Estrada, E. J. Chem. Inf. Comput. Sci. 1996, 36, 844-849; 1997 37, 320-328; 1998, 38, 23-27) employed spectral moments of line graphs in QSPR and QSAR relationship studies of various classes of compounds. A recent paper (Marković, S.; Gutman, I. J. Chem. Inf Comput. Sci. 1999, 39, 289-293) reported that in QSPR and QSAR investigations of benzenoid hydrocarbo...

the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...

we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...

MOTIVATION Molecular diagnostics aims at classifying diseases into clinically relevant sub-entities based on molecular characteristics. Typically, the entities are split into subgroups, which might contain several variants yielding a hierarchical model of the disease. Recent years have introduced a plethora of new molecular screening technologies to molecular diagnostics. As a result molecular ...

The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to ...

Recently, a novel degree-based molecular structure descriptor, called Sombor index was introduced. Let G=(V(G),E(G)) be graph. Then, the of G is defined as SO(G)=?uv?E(G)dG2(u)+dG2(v). In this paper, we give some lemmas that can used to compare indices between two graphs. With these lemmas, determine graph with maximum SO among all cacti n vertices and k cut edges. Furthermore, unique p pendant...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we study the Zagreb indices of n-vertex connected graphs with k cut vertices, the upper bound for M1and M2-values of n-vertex connected graphs with k cut vertices are deter...