Variable Neighborhood Search for Extremal Graphs. 19. Further Conjectures and Results about the Randic Index
Variable Neighborhood Search for Extremal Graphs. 19. Further Conjectures and Results about the Randic Index
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发表时间：
2006-04
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通讯作者：
M. Aouchiche;P. Hansen;M. Zheng
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作者：
M. Aouchiche;P. Hansen;M. Zheng
利用AutoGraphiX 2系统（AGX 2），我们进一步研究了lbn ≤ R i ≤ ubn形式的图不变量之间的关系，其中R表示图G =（V，E）的Randić指数，i是另一个不变量，表示+，−，×，/四种运算之一，lbn和ubn的下界和上界函数的阶为n的图考虑，这是紧的所有n（除了由于边界效应而可能非常小的值）。其中i依次为最大度、最小度和平均度，Δ、δ和d，直径D，围长g，代数连通度和结点连通度，a和ν。在56个猜想中，得到了51个猜想，其中28个是自动证明的，19个是手工证明的，7个是开放的，只有一个被否定。数学与计算机化学竞赛通讯。数学。计算。58（2007）83-102 ISSN 0340 6253
Using the AutoGraphiX 2 system (AGX2), we study further relations between graph invariants of the form lbn ≤ R ⊕ i ≤ ubn where R denotes the Randić index of a graph G = (V, E), i another invariant, ⊕ denotes one of the four operations +,−,×, /, lbn and ubn 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). Here i is in turn maximum, minimum and average degree, Δ, δ and d, diameter D, girth g, algebraic and node connectivity, a and ν, Conjectures are obtained in 51 out of 56 cases, 28 of which are proved automatically, 19 are proved by hand, 7 remain open and only one is refuted. MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 58 (2007) 83-102 ISSN 0340 6253