Topological Properties of Hypercubes
IEEE Transactions on Computers
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Note: The hyper-Wiener index of the generalized hierarchical product of graphs
Discrete Applied Mathematics
Vertex and edge Padmakar-Ivan indices of the generalized hierarchical product of graphs
Discrete Applied Mathematics
Wiener index of some graph operations
Discrete Applied Mathematics
Discrete Applied Mathematics
Note: Further results on hierarchical product of graphs
Discrete Applied Mathematics
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A new operation on graphs is introduced and some of its properties are studied. We call it hierarchical product, because of the strong (connectedness) hierarchy of the vertices in the resulting graphs. In fact, the obtained graphs turn out to be subgraphs of the cartesian product of the corresponding factors. Some well-known properties of the cartesian product, such as reduced mean distance and diameter, simple routing algorithms and some optimal communication protocols are inherited by the hierarchical product. We also address the study of some algebraic properties of the hierarchical product of two or more graphs. In particular, the spectrum of the binary hypertree T"m (which is the hierarchical product of several copies of the complete graph on two vertices) is fully characterized; turning out to be an interesting example of graph with all its eigenvalues distinct. Finally, some natural generalizations of the hierarchic product are proposed.