The Acyclic Polynomial Of A Graph
The acyclic polynomial of a graph.
The adjacency graphs of a complex
The admissable trace problem for E-unitary inverse semigroups.
The algebraic connectivity of two trees connected by an edge of infinite weight.
The algebraic multiplicity of the number zero in the spectrum of a bipartite graph
The all-paths transit function of a graph
A transit function on a set is a function satisfying the axioms , and , for all . The all-paths transit function of a connected graph is characterized by transit axioms.
The alternating sign matrix polytope.
The Analysis of a Nested Dissection Algorithm.
The arc-width of a graph.
The assignment problem with three job categories
The asymptotic behavior of elementary symmetric functions on a probability distribution.
The Balanced Decomposition Number of TK4 and Series-Parallel Graphs
A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f(G) of G is the minimum integer s with the following property: For any balanced colouring of G, there is a partition V (G) = V1 ∪˙ · · · ∪˙ Vr such that, for every i, Vi induces a connected subgraph of order at most s, and contains the same number of red and blue vertices. The function f(G)...
The basis number of some special non-planar graphs
The basis number of a graph was defined by Schmeichel to be the least integer such that has an -fold basis for its cycle space. He proved that for , the basis number of the complete bipartite graph is equal to 4 except for , and with . We determine the basis number of some particular non-planar graphs such as and , , and -cages for , and the Robertson graph.
The b-chromatic number of power graphs.
The B-Domatic Number of a Graph
Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by dominating sets, the parameters corresponding to the chromatic and achromatic numbers are the domatic and adomatic numbers d(G) and ad(G). We introduce the b-domatic number bd(G) as the counterpart of the...
The bias of three pseudo-random shuffles.
The bias of three pseudo-random shuffles. (Short Communication).
The bichromaticity of a graph
The bigraph decomposition number of a graph