AbstractFor given integers n and D, what is the minimum number of edges in a graph on n vertices with the property that after deleting any edge, the remaining graph has diameter no more than D? This problem was first proposed by Murty and Vijayan in 1964. In this paper, we give an exact solution for this problem for general n and D
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases ...
AbstractIf G is a graph on p vertices with connectivity, or edge-connectivity, or minimum valency, a...
We investigate the smallest number λe(G) of edges that can be removed from a non-empty graph G so th...
AbstractFor given integers n and D, what is the minimum number of edges in a graph on n vertices wit...
AbstractIt is proved that, if n is sufficiently large compared with d, then the smallest number of e...
AbstractThe object of this paper is to determine the minimum possible number of edges for a graph of...
We study the following problem: for given integers $d,k$ and graph $G$, can we obtain a graph with d...
AbstractA simple connected graph G with diam(G) = d is said to be ‘vertex diameter-d-critical’ if di...
AbstractLet f(t,k) be the maximum diameter of graphs obtained by deleting t edges from a (t+1)-edge-...
If G is a graph on p vertices with connectivity, or edge-connectivity, or minimum valency, at least ...
We investigate decompositions of a graph into a small number of low-diameter subgraphs. Let P (n, , ...
AbstractWe answer the following question: what is the minimum number of edges of a 2-connected graph...
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases ...
<p>A graph is called diameter-k-critical if its diameter is k, and the removal of any edge strictly ...
Abstract: Let P (t; n) and C(t; n) denote the minimum diameter of a connected graph ob-tained from a...
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases ...
AbstractIf G is a graph on p vertices with connectivity, or edge-connectivity, or minimum valency, a...
We investigate the smallest number λe(G) of edges that can be removed from a non-empty graph G so th...
AbstractFor given integers n and D, what is the minimum number of edges in a graph on n vertices wit...
AbstractIt is proved that, if n is sufficiently large compared with d, then the smallest number of e...
AbstractThe object of this paper is to determine the minimum possible number of edges for a graph of...
We study the following problem: for given integers $d,k$ and graph $G$, can we obtain a graph with d...
AbstractA simple connected graph G with diam(G) = d is said to be ‘vertex diameter-d-critical’ if di...
AbstractLet f(t,k) be the maximum diameter of graphs obtained by deleting t edges from a (t+1)-edge-...
If G is a graph on p vertices with connectivity, or edge-connectivity, or minimum valency, at least ...
We investigate decompositions of a graph into a small number of low-diameter subgraphs. Let P (n, , ...
AbstractWe answer the following question: what is the minimum number of edges of a 2-connected graph...
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases ...
<p>A graph is called diameter-k-critical if its diameter is k, and the removal of any edge strictly ...
Abstract: Let P (t; n) and C(t; n) denote the minimum diameter of a connected graph ob-tained from a...
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases ...
AbstractIf G is a graph on p vertices with connectivity, or edge-connectivity, or minimum valency, a...
We investigate the smallest number λe(G) of edges that can be removed from a non-empty graph G so th...
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