Geodesic
A Note on Path Domination
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 1021-1034

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We study domination between different types of walks connecting two non-adjacent vertices u and v of a graph (shortest paths, induced paths, paths, tolled walks). We succeeded in characterizing those graphs in which every uv-walk of one particular kind dominates every uv-walk of other specific kind. We thereby obtained new characterizations of standard graph classes like chordal, interval and superfragile graphs.
Keywords: domination, paths, geodesics, chordal graphs, interval graphs 
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     author = {Alc\'on, Liliana},
     title = {A {Note} on {Path} {Domination}},
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Alcón, Liliana. A Note on Path Domination. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 1021-1034. http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a17/