Topic
Cartesian product of graphs
About: Cartesian product of graphs is a research topic. Over the lifetime, 276 publications have been published within this topic receiving 3789 citations.
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Book•
14 Apr 2000
TL;DR: Basic Concepts.
Abstract: Basic Concepts. Hypercubes. Hamming Graphs. Cartesian Products. Strong and Direct Products. Lexicographic Products. Fast Recognition Algorithms. Invariants. Appendices. Bibliography. Indexes.
869 citations
TL;DR: In this paper, the authors modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the properties of general graphs, Cartesian product of graphs, random graphs, and some special class of graphs.
Abstract: We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the properties of the Ricci curvature of general graphs, Cartesian product of graphs, random graphs, and some special class of graphs.
251 citations
TL;DR: This work is devoted to evaluating the so-called metric dimension of a finite connected graph, i.e., the minimum cardinality of a resolving set, for a number of graph families, as long as to study its behavior with respect to the join and the cartesian product of graphs.
157 citations
TL;DR: The notion of vertex PI index of a graph is introduced and this notion is applied to compute an exact expression for thePI index of Cartesian product of graphs.
138 citations
TL;DR: A survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamiltonicity, degree sequence and other enumeration results, and their median nature that leads to a fast recognition algorithm is discussed.
Abstract: The Fibonacci cube Γ
n
is the subgraph of the n-cube induced by the binary strings that contain no two consecutive 1s. These graphs are applicable as interconnection networks and in theoretical chemistry, and lead to the Fibonacci dimension of a graph. In this paper a survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamiltonicity, degree sequence and other enumeration results. Their median nature that leads to a fast recognition algorithm is discussed. The Fibonacci dimension of a graph, studies of graph invariants on Fibonacci cubes, and related classes of graphs are also presented. Along the way some new short proofs are given.
128 citations