# Geodetic graphs of diameter two

@article{Blokhuis1988GeodeticGO, title={Geodetic graphs of diameter two}, author={Aart Blokhuis and Andries E. Brouwer}, journal={Geometriae Dedicata}, year={1988}, volume={25}, pages={527-533} }

We survey what is known on geodetic graphs of diameter two and discuss the implications of a new strong necessary condition for the existence of such graphs.

#### 9 Citations

Graphs without even holes or diamonds

- Mathematics
- 2011

An even hole is an induced chordless cycle of even length at least four. A diamond is an induced subgraph isomorphic to K_4-e. We show that graphs without even holes and without diamonds can be… Expand

The independence number for polarity graphs of even order planes

- Mathematics
- 2013

In this paper, we use coherent configurations to obtain new upper bounds on the independence number of orthogonal polarity graphs of projective planes of even order. In the case of classical planes… Expand

Strong geodetic cores and Cartesian product graphs

- Mathematics, Computer Science
- Appl. Math. Comput.
- 2019

It is proved that ${\rm sg}(G \,\square\, K_2) \geq sg(G)$ holds for different families of graphs, a result conjectured to be true in general. Expand

Strong Geodetic Number of Complete Bipartite Graphs, Crown Graphs and Hypercubes

- Mathematics
- Bulletin of the Malaysian Mathematical Sciences Society
- 2019

The strong geodetic number, $$\text {sg}(G),$$ sg ( G ) , of a graph G is the smallest number of vertices such that by fixing a suitable geodesic between each pair of selected vertices, all vertices… Expand

Corrections and additions to the book ‘ Distance-regular Graphs ’

- 2007

This note contains corrections for all errors in [BCN] known to us. Moreover, it provides some additional material and references. Most of the material is presented in the order of appearance in the… Expand

Hyperbolic Bridged Graphs

- Mathematics, Computer Science
- Eur. J. Comb.
- 2002

It is shown that a finite connected bridged graph is 1-hyperbolic if and only if it does not contain any of a list of six graphs as an isometric subgraph. Expand

On nash equilibria for a network creation game

- Mathematics, Computer Science
- SODA '06
- 2006

The tree conjecture is disproved, a constant upper bound on the price of anarchy of <i>O</i>(√α) is derived and characterizations of Nash equilibria are developed and extended to a weighted network creation game as well as to scenarios with cost sharing. Expand

A Delivery Network Creation Game

- Computer Science
- 2009

Each player i optimizes cost(i) = αei + βni + X to maintain short paths to other players while minimizing cost in a non-cooperative network creation game. Expand

Responsive Equilibrium for Self-Adaptive Ubiquitous Interaction

- Computer Science
- ArXiv
- 2019

This work attempts to unify two domains: the Game Theory for cooperative control systems and the Responsive Web Design, under the umbrella of crowdsourcing for information gain on Ubiquous Sytems… Expand