On the number of cut-vertices in a graph.
On the number of orthogonal systems in vector spaces over finite fields.
On the Numbers of Cut-Vertices and End-Blocks in 4-Regular Graphs
A cut-vertex in a graph G is a vertex whose removal increases the number of connected components of G. An end-block of G is a block with a single cut-vertex. In this paper we establish upper bounds on the numbers of end-blocks and cut-vertices in a 4-regular graph G and claw-free 4-regular graphs. We characterize the extremal graphs achieving these bounds.
On the Ramsey-Turán number of finite graphs
On the resilience of long cycles in random graphs.
On the selection of pairs
On the size of minimal unsatisfiable formulas.
On the Spectral Radius of Connected Graphs
On the stability for pancyclicity
A property P defined on all graphs of order n is said to be k-stable if for any graph of order n that does not satisfy P, the fact that uv is not an edge of G and that G + uv satisfies P implies . Every property is (2n-3)-stable and every k-stable property is (k+1)-stable. We denote by s(P) the smallest integer k such that P is k-stable and call it the stability of P. This number usually depends on n and is at most 2n-3. A graph of order n is said to be pancyclic if it contains cycles of all lengths...
On the system of all maximal chains (antichains) of a graph.
On the Turán properties of infinite graphs.
On total restrained domination in graphs
In this paper we initiate the study of total restrained domination in graphs. Let be a graph. A total restrained dominating set is a set where every vertex in is adjacent to a vertex in as well as to another vertex in , and every vertex in is adjacent to another vertex in . The total restrained domination number of , denoted by , is the smallest cardinality of a total restrained dominating set of . First, some exact values and sharp bounds for are given in Section 2. Then the Nordhaus-Gaddum-type...
On vertex stability with regard to complete bipartite subgraphs
A graph G is called (H;k)-vertex stable if G contains a subgraph isomorphic to H ever after removing any of its k vertices. Q(H;k) denotes the minimum size among the sizes of all (H;k)-vertex stable graphs. In this paper we complete the characterization of -vertex stable graphs with minimum size. Namely, we prove that for m ≥ 2 and n ≥ m+2, and as well as are the only -vertex stable graphs with minimum size, confirming the conjecture of Dudek and Zwonek.
On -bounded families of graphs.
One-two descriptor of graphs
Optimal constructions of event-node networks
Ordering the non-starlike trees with large reverse Wiener indices
The reverse Wiener index of a connected graph is defined as where is the number of vertices, is the diameter, and is the Wiener index (the sum of distances between all unordered pairs of vertices) of . We determine the -vertex non-starlike trees with the first four largest reverse Wiener indices for , and the -vertex non-starlike non-caterpillar trees with the first four largest reverse Wiener indices for .
Orthogonal colorings of graphs.