Ana Diánez

Connectivity of graphs with given girth pair

Girth pairs were introduced by Harary and Kovacs [Regular graphs with given girth pair, J. Graph Theory 7 (1983) 209-218]. The odd girth (even girth) of a graph is the length of a shortest odd (even) cycle. Let g denote the smaller of the odd and even girths, and let h denote the larger. Then (g,h) is called the girth pair of the graph. In this paper we prove that a graph with girth pair (g,h) such that g is odd and h>=g+3 is even has high (vertex-)connectivity if its diameter is at most h-3. The edge version of all results is also studied.

The Size of a Graph Without Topological Complete Subgraphs

In this note we show a new upperbound for the function ex(n;TKp), i.e., the maximum number of edges of a graph of order n not containing a subgraph homeomorphic to the complete graph of order p. Further, for

Toughness of the corona of two graphs

{\left \lceil \frac{2n+5}{3}\right \rceil}\leq p

Extremal Graphs without Topological Complete Subgraphs

The toughness of a non-complete graph G=(V, E) is defined as τ(G)=min{|S|/ω(G−S)}, where the minimum is taken over all cutsets S of vertices of G and ω(G−S) denotes the number of components of the resultant graph G−S by deletion of S. The corona of two graphs G and H, written as G° H, is the graph obtained by taking one copy of G and |V(G)| copies of H, and then joining the ith vertex of G to every vertex in the ith copy of H. In this paper, we investigate the toughness of this kind of graphs and obtain the exact value for the corona of two graphs belonging to some families as paths, cycles, stars, wheels or complete graphs.

The Menger number of the strong product of graphs

The exact values of the function

Size of Graphs with High Girth

ex(n;TK_{p})

The center of an infinite graph

are known for

On the restricted connectivity and superconnectivity in graphs with given girth

{\lceil \frac{2n+5}{3}\rceil}\leq p < n

Sufficient conditions for λ′-optimality of graphs with small conditional diameter

(see [Cera, Dianez, and Marquez, SIAM J. Discrete Math., 13 (2000), pp. 295--301]), where

Diameter-girth sufficient conditions for optimal extraconnectivity in graphs

ex(n;TK_p)