
A set
Let
A total dominating function (TDF) of a graph
Vertex elimination orderings play a central role in many portions of graph theory and are exemplified by the so-called `perfect elimination orderings’ of chordal graphs. But perfect elimination orderings and chordal graphs enjoy many special advantages that overlap in more general settings: the random way that simplicial vertices can be chosen, always having a choice of simplicial vertices, the hereditary nature of being simplicial, and the neutral effect of deleting a simplicial vertex on whether the graph is chordal. A graph metatheory of vertex elimination formalizes such distinctions for general vertex elimination and examines them with simple theorems and delineating counterexamples.
In this paper we give a survey of all graphs of order
The edge-bandwidth of a graph
Let
Let
Suppose
The square
Given any positive integer
Let
An efficient method for generating level sequence representations of rooted trees in a well-defined order was developed by Beyer and Hedetniemi. In this paper, we extend Beyer and Hedetniemi’s approach to produce an algorithm for parallel generation of rooted trees. This is accomplished by defining the lexicographic distance between two rooted trees to be the number of rooted trees between them in the ordering of trees produced by the Beyer and Hedetniemi algorithm. Formulas are provided for the lexicographic distance between rooted trees with certain structures. In addition, we present algorithms for ranking and unranking rooted trees based on the ordering of the trees that is induced by the Beyer and Hedetniemi generation algorithm.
A fall coloring of a graph
For a positive integer
The covering number for a subset of leaves in a finite rooted tree is defined as the number of subtrees which remain after deleting all the paths connecting the root and the other leaves. We find the formula for the total sum (hence the average) of the covering numbers for a given subset of labeled leaves over all unordered binary trees with
1970-2025 CP (Manitoba, Canada) unless otherwise stated.