# Search results for: Wyatt J. Desormeaux

Indian Journal of Pure and Applied Mathematics > 2018 > 49 > 2 > 349-364

*G*is the minimum number of vertices required to dominate the vertices of

*G*. Due to the minimality of γ, if a set of vertices of

*G*has cardinality less than γ then there are vertices of G that are not dominated by that set. The

*k*-domination defect of

*G*is the minimum number...

Discussiones Mathematicae Graph Theory > 2017 > 38 > 1 > 203-215

Discrete Applied Mathematics > 2017 > 223 > C > 52-63

Discussiones Mathematicae Graph Theory > 2016 > 36 > 4 > 1043-1050

Discrete Applied Mathematics > 2016 > 207 > C > 39-44

Journal of Combinatorial Optimization > 2016 > 31 > 1 > 52-66

Discrete Applied Mathematics > 2014 > 177 > Complete > 88-94

Discrete Mathematics > 2014 > 319 > Complete > 15-23

Discrete Applied Mathematics > 2013 > 161 > 18 > 2925-2931

Journal of Graph Theory > 75 > 1 > 91 - 103

*G*is the minimum cardinality of a set

*S*of vertices, so that every vertex of

*G*is adjacent to a vertex in

*S*. In this article, we determine an optimal upper bound on the total domination number of a graph with diameter 2. We show that for every graph

*G*on

*n*vertices with diameter 2, ${\gamma}_{t}\left(G\right)\le 1+\sqrt{nln\left(n\right)}$. This bound is optimal in the sense that given any $\epsilon >0$...

Discrete Applied Mathematics > 2013 > 161 > 3 > 349-354

Journal of Combinatorial Optimization > 2013 > 25 > 1 > 47-59

*u*and

*v*be vertices of a graph

*G*, such that the distance between

*u*and

*v*is two and

*x*is a common neighbor of

*u*and

*v*. We define the edge lift of

*uv*off

*x*as the process of removing edges

*ux*and

*vx*while adding the edge

*uv*to

*G*. In this paper, we investigate the effect that edge lifting has on the total domination number of a graph. Among other results, we show that there are no trees for which...

Discrete Applied Mathematics > 2011 > 159 > 15 > 1548-1554

Discrete Applied Mathematics > 2011 > 159 > 10 > 1048-1052

Discrete Mathematics > 2010 > 310 > 24 > 3446-3454

Discrete Applied Mathematics > 2010 > 158 > 15 > 1587-1592