A new type of decomposition of graphs – the operator decomposition connected with the classical notion of homogeneous set (or module) is introduced. The properties of this decomposition are described. Using this decomposition we prove the following. Let P and Q be two hereditary graph classes such that P is closed with respect to the operation of join and Q is closed with respect to the operati...

A modified k-deck of a graph G is obtained by removing k edges of G in all possible ways, and adding k (not necessarily new) edges in all possible ways. Krasikov and Roditty asked if it was possible to construct the usual k-edge deck of a graph from its modified k-deck. Earlier I solved this problem for the case when k = 1. In this paper, the problem is completely solved for arbitrary k. The pr...

A modified k-deck of a graph is obtained by removing k edges in all possible ways and adding k (not necessarily new) edges in all possible ways. Krasikov and Roditty used these decks to give an independent proof of Müller’s result on the edge reconstructibility of graphs. They asked if a k-edge deck could be constructed from its modified k-deck. In this paper, we solve the problem when k = 1. W...

They are unlike conventional vehicles, which powered by internal combustion engines, electric vehicles use electricity stored in rechargeable batteries or fuel cells to power the motor. Electric have become increasingly popular recent years due their lower environmental impact and potential reduce greenhouse gas emissions. also more efficient than traditional gasoline- can save drivers money on...

Background: Enterovirus (EV) infections are one of the most common causes of aseptic meningitis in pediatrics. To diagnose EV meningitis, virus isolation in cell cultures is often time consuming and lacks sensitivity to be of clinical relevance. This makes the virus culture results difficult to interpret. The rapid detection of EVs in cerebrospinal fluid (CSF) by molecular diagnostic techniques...

A graph is said to be reconstructible if it is determined up to isomorphism from the collection of all its one-vertex deleted unlabeled subgraphs. The Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that all triangle-free graphs G with connectivity two such that diam(G) = 2 or diam(G) = diam(G) = 3 are reconstructibl...