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Permanent of a matrix – a combinatorial study of graphs. (English) Zbl 1161.68695

Summary: We study graphs using a combinatorial approach, the permanent of a matrix. The permanent of an \(m\times n\) matrix \(A=(a_{ij})\) with \(m\leq n\) is defined as \(\sum a_{1i_1},a_{2i_2},\dots,a_{mi_m}\) where the summation runs through the \(m\)-permutations \((i_1,i_2,\dots,i_m)\) of \(1,2,3,\dots,n\). The permanent of the adjacency matrix of various graphs is computed using Mathlab and also the variation of the permanent of the adjacency matrix of a graph with respect to the number of edges of the graph is analyzed.

MSC:

68R10 Graph theory (including graph drawing) in computer science
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A15 Determinants, permanents, traces, other special matrix functions
68W30 Symbolic computation and algebraic computation
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