# Search results for: Simon Jäger

Discrete Mathematics > 2018 > 341 > 1 > 119-125

Discrete Mathematics > 2017 > 340 > 11 > 2650-2658

Discrete Optimization > 2017 > 23 > C > 81-92

Discrete Mathematics > 2018 > 341 > 1 > 119-125

A prominent parameter in the context of network analysis, originally proposed by Watts and Strogatz (1998), is the clustering coefficient of a graph G . It is defined as the arithmetic mean of the clustering coefficients of its vertices, where the clustering coefficient of a vertex u of G is the relative density m ( G [ N G ( u ) ] ) ∕ d G ( u ) 2 of its neighborhood...

Discrete Mathematics > 2017 > 340 > 11 > 2650-2658

For a set S of vertices of a graph G , a vertex u in V ( G ) ∖ S , and a vertex v in S , let dist ( G , S ) ( u , v ) be the distance of u and v in the graph G − ( S ∖ { v } ) . Dankelmann et al. (2009) define S to be an exponential dominating set of G if w ( G , S ) ( u ) ≥ 1 for every vertex u in V ( G ) ∖ S , where w ( G , S ) ( u...

Discrete Optimization > 2017 > 23 > C > 81-92

The domination number γ(G) of a graph G, its exponential domination number γe(G), and its porous exponential domination number γe∗(G) satisfy γe∗(G)≤γe(G)≤γ(G). We contribute results about the gaps in these inequalities as well as the graphs for which some of the inequalities hold with equality. Relaxing the natural integer linear program whose optimum value is γe∗(G), we are led to the definition...