1,187 research outputs found
The generalized 3-edge-connectivity of lexicographic product graphs
The generalized -edge-connectivity of a graph is a
generalization of the concept of edge-connectivity. The lexicographic product
of two graphs and , denoted by , is an important graph
product. In this paper, we mainly study the generalized 3-edge-connectivity of
, and get upper and lower bounds of .
Moreover, all bounds are sharp.Comment: 14 page
Steiner Distance in Product Networks
For a connected graph of order at least and , the
\emph{Steiner distance} among the vertices of is the minimum size
among all connected subgraphs whose vertex sets contain . Let and be
two integers with . Then the \emph{Steiner -eccentricity
} of a vertex of is defined by . Furthermore, the
\emph{Steiner -diameter} of is . In this paper, we investigate the Steiner distance and Steiner
-diameter of Cartesian and lexicographical product graphs. Also, we study
the Steiner -diameter of some networks.Comment: 29 pages, 4 figure
Monomials, Binomials, and Riemann-Roch
The Riemann-Roch theorem on a graph G is related to Alexander duality in
combinatorial commutive algebra. We study the lattice ideal given by chip
firing on G and the initial ideal whose standard monomials are the G-parking
functions. When G is a saturated graph, these ideals are generic and the Scarf
complex is a minimal free resolution. Otherwise, syzygies are obtained by
degeneration. We also develop a self-contained Riemann-Roch theory for artinian
monomial ideals.Comment: 18 pages, 2 figures, Minor revision
- …