Geodesic
Properties of paths in graphs and multigraphs
Prikladnaâ diskretnaâ matematika, no. 1 (2010), pp. 118-124

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The length of the shortest full path in a strongly connected orgraph with $n$ vertices is estimated. The exponent of the vertex incedent matrix of the graph with self-loop is estimated too. A polynomial estimate is obtained for the subexponent of the system of vertex incedent matrices of $n$-vertex graphs whose union is a strongly connected graph. These results can be used to investigate essential variables of the coordinate functions which define compositions of transformations of the set of finite words.
Keywords: full path, shortest path, exponent
Mots-clés : subexponent. 
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     author = {V. M. Fomichev},
     title = {Properties of paths in graphs and multigraphs},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {118--124},
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     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_1_a8/}
}
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V. M. Fomichev. Properties of paths in graphs and multigraphs. Prikladnaâ diskretnaâ matematika, no. 1 (2010), pp. 118-124. http://geodesic.mathdoc.fr/item/PDM_2010_1_a8/