Double graphs

TL;DR: In this paper, the authors defined the resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a (unit) resistor.

TL;DR: It is shown that a strong input can make the neurons almost independent, suggesting that functional connectivity does not depend only on the static anatomical connectivity, but also on the external inputs.

TL;DR: In this paper, the authors studied spectra, energy and Laplacian energy of the strong double graph SD(G) and derived a formula for the number of spanning trees in terms of the spectral energy of a graph.

TL;DR: In this paper , the authors generalized two existing graph operations, namely, the corona product and double graph operation, and used these newly developed graph operations to create two complex structures by using two graph operations.

TL;DR: In this article, the authors introduce algebraic graph theory and show that the spectrum of a graph can be modelled as a graph graph, and the spectrum can be represented as a set of connected spanning trees.

TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.

TL;DR: This chapter discusses the structure of Composition, the partial order of Graphs and Homomorphisms, and testing for the Existence of Homomorphism.

TL;DR: Cameron et al. as mentioned in this paper introduced the concept of graph Laplacians and showed that they can be used to construct strong regular graphs and distance-transitive graphs, including Cayley graphs.