Transitive, Locally Finite Median Graphs with Finite Blocks

Abstract

The subject of this paper are infinite, locally finite, vertex-transitive median graphs. It is shown that the finiteness of the -classes of such graphs does not guarantee finite blocks. Blocks become finite if, in addition, no finite sequence of -contractions produces new cutvertices. It is proved that there are only finitely many vertex-transitive median graphs of given finite degree with finite blocks. An infinite family of vertex-transitive median graphs with finite intransitive blocks is also constructed and the list of vertex-transitive median graphs of degree four is presented.

On Pairwise Kernels: An Efficient Alternative and Generalization Analysis

“…The pairwise kernel matrix can be interpreted as a weighted adjacency matrix of the Kronecker product graph [8] of the two graphs whose weighted adjacency matrices are the instance-wise kernel matrices. Therefore, we refer to this pairwise kernel as Kronecker kernel to distinguish from the one we will propose in the next section.…”

“…So, it is natural to imagine that we can design another pairwise kernel based on another kind of product graph. In this paper, we adopt another kind of product graph called Cartesian product graph [8]. Assume that we have two graphs G (1) and G (2) whose sets of nodes are V (1) and V (2) , respectively.…”

Operations on M-Strong Fuzzy Graphs.

“…[1,4] Many interesting graphs are obtained fromcomposing simpler graphs via several operations. For more information on graph operations see [3].…”

Distance Magic Labeling and Two Products of Graphs

“…The main topic of this paper is the direct product (that is known also by many other names, see [6]). It is the most natural graph product in the sense that each edge of G × H projects to an edge in both factors G and H .…”

“…This is not so rare and also in this work we show that it is enough for one factor to be a distance magic graph with one additional property and then the product with any regular graph will result in a distance magic graph. More details about the direct product and products in general can be found in the book [6].…”