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- W2964715235 abstract "The construction of new graphs starting from smaller factor graphs is a very natural and fruitful technique, largely developed in the literature for its theoretical interest, but also for its practical applications. There exist four classical graph products – the Cartesian, the direct, the strong, the lexicographic product – whose structure and applicability are quite surprising. Furthermore, many graph operations can be expressed in terms of NEPS (non-complete extended p-sum) and the corresponding spectra are easy to obtain by combining the eigenvalues of the factors. A natural question within graph products is in fact to determine spectral and topological properties of the compound graph when the corresponding properties of the factors are known or given. This talk is about the wreath product of finite graphs, a relatively recent graph operation which cannot be interpreted as NEPS: this is an analogue of the classical wreath product of groups, also related to Probability theory via the notion of Lamplighter random walk. After giving some basic definitions, we illustrate the adjacency matrix of a wreath product, which can be expressed in terms of sums of Kronecker product of matrices, and we show that by specializing the structure of the factors the spectrum can be elegantly computed for some infinite classes of graphs, by using a reduction argument. Then we focus on the computation of some degree-based and distance-based invariants. Our strategy in the investigation of distances essentially involves some special functions computing the length of some paths visiting at least once the vertices of a prescribed vertex subset of the first factor. This is also a tool to study total distances and their connections with the distance balanced property. Some open problems are also described. The present talk is a collection of results obtained in some recent works joint with F. Belardo (University of Naples Federico II), M. Cavaleri and A. Scozzari (Unicusano Roma) and D. D'Angeli (TUGraz)." @default.
- W2964715235 created "2019-08-13" @default.
- W2964715235 creator A5014663908 @default.
- W2964715235 date "2018-08-13" @default.
- W2964715235 modified "2023-09-25" @default.
- W2964715235 title "Wreath product of graphs: Topological Indices and Spectrum" @default.
- W2964715235 hasPublicationYear "2018" @default.
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