A block of a graph is a nonseparable maximal subgraph of the graph. We denote by bG the number of block of a graph G. We show that, for a connected graph G of order n with minimum degree k≥1, bG<2k−3/k2−k−1n. The bound is asymptotically tight. In addition, for a connected cubic graph G of order n≥14, bG≤n/2−2. The bound is tight
Let G be a finite connected graph. We give an asymptotically tight upper bound on the size of G in t...
AbstractThe maximum number of cutvertices in a connected graph of order n having minimum degree at l...
For any graph = , , block graph is a graph whose set of vertices is the union of the set o...
AbstractA k-block is a maximal k-vertex-connected subgraph, and a k-block which does not contain a (...
AbstractA graph with n vertices and minimum degree k⩾2 can contain no more than (2k−2)n(k2−2) cut ve...
We investigate what conditions on the minimum or average degree of a graph ensure that it contains a...
Consider the class of graphs on n vertices which have maximum degree at most 1/2 n - 1 + τ, where τ ...
In this paper we show that if G is a 2-connected graph having minimum degree n such that |V(G)|;≥2n+...
AbstractIn this paper we show that if G is a 2-connected graph having minimum degree n such that |V(...
In this paper we show that if G is a 2-connected graph having minimum degree n and at least 2n verti...
The average size of connected vertex subsets of a connected graph generalises a much-studied paramet...
The average size of connected vertex subsets of a connected graph generalises a much-studied paramet...
Let G be a simple graph, and let p be a positive integer. A subset D ⊆ V(G) is a p-dominating set of...
We investigate the smallest number λe(G) of edges that can be removed from a non-empty graph G so th...
AbstractLet G=(V,E) be a graph. A set S⊆V is a restrained dominating set if every vertex in V−S is a...
Let G be a finite connected graph. We give an asymptotically tight upper bound on the size of G in t...
AbstractThe maximum number of cutvertices in a connected graph of order n having minimum degree at l...
For any graph = , , block graph is a graph whose set of vertices is the union of the set o...
AbstractA k-block is a maximal k-vertex-connected subgraph, and a k-block which does not contain a (...
AbstractA graph with n vertices and minimum degree k⩾2 can contain no more than (2k−2)n(k2−2) cut ve...
We investigate what conditions on the minimum or average degree of a graph ensure that it contains a...
Consider the class of graphs on n vertices which have maximum degree at most 1/2 n - 1 + τ, where τ ...
In this paper we show that if G is a 2-connected graph having minimum degree n such that |V(G)|;≥2n+...
AbstractIn this paper we show that if G is a 2-connected graph having minimum degree n such that |V(...
In this paper we show that if G is a 2-connected graph having minimum degree n and at least 2n verti...
The average size of connected vertex subsets of a connected graph generalises a much-studied paramet...
The average size of connected vertex subsets of a connected graph generalises a much-studied paramet...
Let G be a simple graph, and let p be a positive integer. A subset D ⊆ V(G) is a p-dominating set of...
We investigate the smallest number λe(G) of edges that can be removed from a non-empty graph G so th...
AbstractLet G=(V,E) be a graph. A set S⊆V is a restrained dominating set if every vertex in V−S is a...
Let G be a finite connected graph. We give an asymptotically tight upper bound on the size of G in t...
AbstractThe maximum number of cutvertices in a connected graph of order n having minimum degree at l...
For any graph = , , block graph is a graph whose set of vertices is the union of the set o...
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