Geodesic
Connectivity of Path Graphs
Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 1 
D. Ferrero. Connectivity of Path Graphs. Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a4/
@article{AMUC_2003_72_1_a4,
     author = {D. Ferrero},
     title = {Connectivity of {Path} {Graphs}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2003},
     volume = {72},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a4/}
}
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Voir la notice de l'article provenant de la source Comenius University

The aim of this paper is to lower bound the connectivity of $k$-path graphs. From the bounds obtained, we give conditions to guarantee maximum connectivity. Then, it is shown that those maximally connected graphs satisfying the previous conditions are also super-$\lambda$. While doing so, we derive some properties about the girth and the diameter of path graphs. Finally, the results are extended to path graphs resulting from the iteration of the $k$-path graph operator.