21,849 research outputs found
On the independent domination number of graphs with given minimum degree
AbstractWe prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that of Haviland (1991) and settles the case δ = 2 of the corresponding conjecture by Favaron (1988)
On the algorithmic complexity of twelve covering and independence parameters of graphs
The definitions of four previously studied parameters related to total coverings and total matchings of graphs can be restricted, thereby obtaining eight parameters related to covering and independence, each of which has been studied previously in some form. Here we survey briefly results concerning total coverings and total matchings of graphs, and consider the aforementioned 12 covering and independence parameters with regard to algorithmic complexity. We survey briefly known results for several graph classes, and obtain new NP-completeness results for the minimum total cover and maximum minimal total cover problems in planar graphs, the minimum maximal total matching problem in bipartite and chordal graphs, and the minimum independent dominating set problem in planar cubic graphs
Coloring, location and domination of corona graphs
A vertex coloring of a graph is an assignment of colors to the vertices
of such that every two adjacent vertices of have different colors. A
coloring related property of a graphs is also an assignment of colors or labels
to the vertices of a graph, in which the process of labeling is done according
to an extra condition. A set of vertices of a graph is a dominating set
in if every vertex outside of is adjacent to at least one vertex
belonging to . A domination parameter of is related to those structures
of a graph satisfying some domination property together with other conditions
on the vertices of . In this article we study several mathematical
properties related to coloring, domination and location of corona graphs.
We investigate the distance- colorings of corona graphs. Particularly, we
obtain tight bounds for the distance-2 chromatic number and distance-3
chromatic number of corona graphs, throughout some relationships between the
distance- chromatic number of corona graphs and the distance- chromatic
number of its factors. Moreover, we give the exact value of the distance-
chromatic number of the corona of a path and an arbitrary graph. On the other
hand, we obtain bounds for the Roman dominating number and the
locating-domination number of corona graphs. We give closed formulaes for the
-domination number, the distance- domination number, the independence
domination number, the domatic number and the idomatic number of corona graphs.Comment: 18 page
Degree Sequence Index Strategy
We introduce a procedure, called the Degree Sequence Index Strategy (DSI), by
which to bound graph invariants by certain indices in the ordered degree
sequence. As an illustration of the DSI strategy, we show how it can be used to
give new upper and lower bounds on the -independence and the -domination
numbers. These include, among other things, a double generalization of the
annihilation number, a recently introduced upper bound on the independence
number. Next, we use the DSI strategy in conjunction with planarity, to
generalize some results of Caro and Roddity about independence number in planar
graphs. Lastly, for claw-free and -free graphs, we use DSI to
generalize some results of Faudree, Gould, Jacobson, Lesniak and Lindquester
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