The transmission of a vertex v (chemical) graph G is the sum distances from to other vertices in G. If any two have different transmissions, then irregular graph. It shown that for odd number n≥7 there exists chemical tree order n. A construction provided which generates new trees. Two additional families graphs are characterized by property irregularity and sufficient condition guarantee prese...

One of the greatest challenges in bioinformatics is to shed light on the relationship between genomic and chemical significances of metabolic pathways. Here, we demonstrate two types of chemical structure search servers: SIMCOMP (http://www.genome.jp/tools/simcomp/) for the chemical similarity search and SUBCOMP (http://www.genome.jp/tools/subcomp/) for the chemical substructure search, where b...

In this paper, we introduce a novel graph polynomial called the 'information polynomial' of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform ...

The development of chemical applications of graph theory is reviewed from a personal perspective. Graph-theoretical methods for finding all graphs fulfilling certain mathematical conditions followed by eliminating chemically impossible solutions are equivalent to the ‘Sherlock Holmes principle’. For molecular graphs, this is illustrated by monocyclic aromatic systems and by valence isomers of a...

Graphs can be used to represent such diverse entities as chemical compounds, transportation networks, and the world wide web. Stochastic graph grammars are compact representations of probability distributions over graphs. We present an algorithm for inferring stochastic graph grammars from data. That is, given a set of graphs that, for example, correspond to a set of chemical compounds, all of ...

Similarity search in databases of labeled graphs is a fundamental task in managing graph data such as XML, chemical compounds and social networks. Typically, a graph is decomposed to a set of substructures (e.g., paths, trees and subgraphs) and a similarity measure is defined via the number of common substructures. Using the representation, graphs can be stored in a document database by regardi...

I was born in Zagreb (Croatia) on October 26, 1936. My parents were Regina (née Pavić) (April17, 1916, Zagreb–March 9, 1992, Zagreb) and Cvjetko Trinajstić (September 9, 1913, Volosko–October 29, 1998, Richmond, Australia).