Quantum probability aspects to lexicographic and strong products of graphs. (English) Zbl 1452.05186
Summary: The adjacency matrix of the lexicographic product of graphs is decomposed into a sum of monotone independent random variables in a certain product state. The adjacency matrix of the strong product of graphs admits an expression in terms of commutative independent random variables in a product state. Their spectral distributions are obtained by using the monotone, classical and Mellin convolutions of probability distributions.
MSC:
| 05D40 | Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) |
| 05C76 | Graph operations (line graphs, products, etc.) |
| 05C30 | Enumeration in graph theory |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 81S25 | Quantum stochastic calculus |
Keywords:
adjacency matrix; convolution of probability distributions; lexicographic product; spectral distribution; strong productReferences:
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