Lower bounds for the number of bends in three-dimensional orthogonal graph drawings.
The open neighborhood of an edge in a graph is the set consisting of all edges having a common end-vertex with . Let be a function on , the edge set of , into the set . If for each , then is called a signed edge total dominating function of . The minimum of the values , taken over all signed edge total dominating function of , is called the signed edge total domination number of and is denoted by . Obviously, is defined only for graphs which have no connected components...
LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of this generalization....
L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.