منابع مشابه
Radius, diameter, and minimum degree
We give asymptotically sharp upper bounds for the maximum diameter and radius of (i) a connected graph, {ii) a connected trangle-free graph, (iii) a connected C,-free graph with n vertices and with minimum degree 6, where n tends to infinity. Some conjectures for J&-free graphs are also stated. Let G be a connected graph with vertex set V(G) and edge set E(G). For any XJJ E V(G) let dG(x,y) den...
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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 ...
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We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G. Let G be a graph of order n and λ (G) be the spectral radius of its adjacency matrix. One of the main results of the paper is the following theorem: Let k 2, n k3 + k + 4, and let G be a graph of order n, with minimum degree δ (G) k. If λ (G) n k 1, then G has a Hamiltonian cycle, unless G = K1 _ (Kn 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 ...
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a r t i c l e i n f o a b s t r a c t In this paper, we study the problem of computing a spanning tree of a given undirected disk graph such that the radius of the tree is minimized subject to a given degree constraint *. We first introduce an (8, 4)-bicriteria approximation algorithm for unit disk graphs (which is a special case of disk graphs) that computes a spanning tree such that the degre...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1989
ISSN: 0095-8956
DOI: 10.1016/0095-8956(89)90066-x