Recherche à voisinage variable de graphes extrémaux 26. Nouveaux résultats sur la maille
RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 4, pp. 339-358.

On étudie à l’aide du système AutoGraphiX 2 (AGX 2) des relations de la forme

b ̲ n gib ¯ n
g désigne la maille d’un graphe G=(V,E), i un autre invariant parmi la distance moyenne l ¯, l’index λ 1 , l’indice de Randić R et le nombre de domination β, désigne l’une des opérations +,-,×,/, b ̲ n et b ¯ n des fonctions de l’ordre n du graphe qui bornent l’expression gi et sont atteintes pour tout n (sauf éventuellement de très petites valeurs du fait des effets de bord). Les résultats prouvés ou discutés ci-dessous ont déjà été présentés, sous forme de conjectures, dans un article précédent paru dans RAIRO Recherche Opérationnelle [RAIRO Oper. Res. 39 (2005) 275-293].

Using the AutoGraphiX 2 system (AGX2), we study relations between graph invariants of the form

b ̲ n gib ¯ n
where g denotes the girth of a graph G=(V,E), i another invariant among the average distance l ¯, the index λ 1 , the Randić index R and the domination number β, denotes one of the four operations +,-,×,/, b ̲ n and b ¯ n lower and upper bounding functions of the order n of the graph considered which are tight for all n (except possibly very small values due to border effects). The results proved or discussed below were first presented as conjectures in a previous paper published in RAIRO Operations Research [RAIRO Oper. Res. 39 (2005) 275-293].

DOI : 10.1051/ro/2009022
Classification : 05C35, 05C12
Keywords: graph, AGX, girth, distance, Randić, index, domination
Mots clés : graphe, AGX, maille, distance, Randić, index, domination
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     title = {Recherche \`a voisinage variable de graphes extr\'emaux 26. {Nouveaux} r\'esultats sur la maille},
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Aouchiche, Mustapha; Favaron, Odile; Hansen, Pierre. Recherche à voisinage variable de graphes extrémaux 26. Nouveaux résultats sur la maille. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 4, pp. 339-358. doi : 10.1051/ro/2009022. http://www.numdam.org/articles/10.1051/ro/2009022/

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