منابع مشابه
Diameter vulnerability of GC graphs
Concern over fault tolerance in the design of interconnection networks has stimulated interest in finding large graphs with maximum degree ∆ and diameter D such that the subgraphs obtained by deleting any set of s vertices have diameter at most D′, this value being close to D or even equal to it. This is the so-called (∆, D, D′, s)-problem. The purpose of this work has been to study this proble...
متن کاملDiameter vulnerability of graphs by edge deletion
Let f (t, k) be the maximum diameter of graphs obtained by deleting t edges from a (t+1)-edge-connected graph with diameter k. This paper shows 4 √ 2t−6 < f (t, 3) ≤ max{59, 5 √ 2t+7} for t ≥ 4, which corrects an improper result in [C. Peyrat, Diameter vulnerability of graphs, Discrete Appl. Math. 9 (3) (1984) 245–250] and also determines f (2, k) = 3k − 1 and f (3, k) = 4k − 2 for k ≥ 3. c © 2...
متن کاملOn 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 کاملOriented diameter of graphs with diameter 3
In 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has an orientation with diameter at most 6. They also gave general bounds on the smallest value f(d) such that every 2-edge-connected graph G with diameter d has an orientation with diameter at most f(d). For d = 3, their general bounds reduce to 8 ≤ f(3) ≤ 24. We improve these bounds to 9 ≤ f(3) ≤ 11.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1984
ISSN: 0166-218X
DOI: 10.1016/0166-218x(84)90024-6