We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

This paper proposes an entropy-based best tree decomposition and reconstruction method for signals on graphs. A recently popular method for graph signal decomposition is to down-sample and filter a graph signal by low-pass and high-pass filters, then iterate decomposition on every low-pass component. This method is not well-suited for graph signals with significant high frequency components. We...

The problem of arbitrary decomposition of a graph G into closed trails i.e. a decomposition into closed trails of prescribed lengths summing up to the size of the graph G was first considered in the case of the complete graph G = Kn (for odd n) in connection with vertexdistinguishing coloring of the union of cycles. Next, the same problem was investigated for other families of graphs. In this p...

Ear decomposition of a graph has been extensively studied in relation to graph connectivity. In this paper, a connection of ear decomposition to graph embeddings is exhibited. It is shown that constructing a maximum-paired ear decomposition of a graph and constructing a maximum-genus embedding of the graph are polynomial-time equivalent. Applications of this connection are discussed.