
The chromatic polynomial captures a good deal of combinatorial information about a graph, describing its acyclic orientations, its all-terminal reliability, its spanning trees, as well as its colorings. Several methods for computing the chromatic polynomial of a graph G construct a computation tree for G whose leaves are “simple” base graphs for which the chromatic polynomial is readily found. Previously studied methods involved base graphs which are complete graphs, completely disconnected graphs, forests, and trees. In this paper, we consider chordal graphs as base graphs. Algorithms for computing the chromatic polynomial based on these concepts are developed, and computational results are presented.
Using several computer algorithms, we calculate some values and bounds for the function
We give some results on the excess of Hadamard matrices. We provide a list for Hadamard matrices of order
The type of a
Let
The structure and the hamiltonicity of vertex-transitive graphs of order
In this paper, the algorithm developed in
Consider combinations of
The minimum cardinality of a pairwise balanced design on nineteen points is determined; a minimal design is exhibited containing
It is shown that the collection of all the
A
The cost of a sorting algorithm is the number of primitive operations used in a worst-case execution of the algorithm. In the standard model, the primitive operation is a binary comparison, which sorts a pair of keys. Cost measures based on other primitive operations are considered. A general lower bound for the cost of a sorting algorithm is given, which is valid for a wide class of possible primitives. For several special primitive operations, sorting algorithms are given. The primitive operations studied are: sorting
Hartman and Rosa have shown that the complete graph
The integrity of a graph
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