منابع مشابه
On Diameter of Line Graphs
The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
متن کاملDiameter Two Graphs of Minimum Order with Given Degree Set
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
متن کاملThe Diameter of Random Graphs
Extending some recent theorems of Klee and Larman, we prove rather sharp results about the diameter of a random graph. Among others we show that if d = d(n) > 3 and m = m(n) satisfy (log n)/d 3 log log n -> oo, 2rf_Imd'/'nd+x log n -» oo and dd~2md~l/nd — log n -» -oo then almost every graph with n labelled vertices and m edges has diameter d. About twenty years ago Erdös [7], [8] used random g...
متن کاملThe diameter of Hanoi graphs
Many questions regarding the Tower of Hanoi problem have been posed and answered during the years. Variants of the classical puzzle, such as allowing more than 3 pegs, and imposing limitations on the possible moves among the pegs, raised the analogous questions for those variants. One such question is: given a variant, and a certain number of disks, find a pair of disk arrangements such that th...
متن کاملTesting the Diameter of Graphs
We propose a general model for testing graph properties, which extends and simpliies the bounded degree model of GR97]. In this model we present a family of algorithms that test whether the diameter of a graph is bounded by a given parameter D, or is-far from any graph with diameter at most (D). The function (D) ranges between D + 4 and 4D + 2, depending on the algorithm. All our algorithms run...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1998
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(98)00041-9