Distance domination and generalized eccentricity in graphs with given minimum degree
نویسندگان
چکیده
منابع مشابه
Diameter 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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We prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that by J. Haviland 3] and settles Case = 2 of the corresponding conjecture by O. Favaron 2].
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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Let γ(n, δ) denote the maximum possible domination number of a graph with n vertices and minimum degree δ. Using known results we determine γ(n, δ) for δ = 0, 1, 2, 3, n ≥ δ +1 and for all n, δ where δ = n − k and n is sufficiently large relative to k. We also obtain γ(n, δ) for all remaining values of (n, δ) when n ≤ 14 and all but 6 values of (n, δ) when n = 15 or 16.
متن کاملTight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II
Let γ(n, δ) denote the largest possible domination number for a graph of order n and minimum degree δ. This paper is concerned with the behavior of the right side of the sequence n = γ(n, 0) ≥ γ(n, 1) ≥ · · · ≥ γ(n, n− 1) = 1. We set δk(n) = max{δ | γ(n, δ) ≥ k}, k ≥ 1. Our main result is that for any fixed k ≥ 2 there is a constant ck such that for sufficiently large n, n− ckn ≤ δk+1(n) ≤ n− n...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2019
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22503