Related papers: Basis condition for generalized spline modules
A connected and nonempty graph A is defined as generalized t-edge distance-balanced, while for each edge f={\alpha}\{beta} the number of edges nearer to {\alpha} than \{beta} are equal to t-times of edges nearer to \{beta} than to {\alpha},…
A graph $\Gamma$ labelled by a set $S$ defines a group $G(\Gamma)$ whose generators are the set of labels $S$ and whose relations are all words which can be read on closed paths of this graph. We introduce the notion of aspherical graph and…
Given an edge-coloring of a graph $G$, we associate to every vertex $v$ of $G$ the set of colors appearing on the edges incident with $v$. The palette index of $G$ is defined as the minimum number of such distinct sets, taken over all…
A vertex $v$ is called an AR-vertex, if $v$ has distinct edge weight sums for each distinct subset of edges incident on $v$. i.e., if $\{x_1,x_2,\dots,x_k\}$ are the edge labels of the edges incident on $v$, then the $2^k$ subset sums are…
This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$-compatible map for the pairs of a complete graph and an arbitrary graph, and using it, we give a combinatorial lower bound for the…
Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical properties of the measured signals. Conditions…
We compute the depth and (give bounds for) the regularity of generalized binomial edge ideals associated with generalized block graphs.
The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered…
In the literature, the notion of discrepancy is used in several contexts, even in the theory of graphs. Here, for a graph $G$, $\{-1, 1\}$ labels are assigned to the edges, and we consider a family $\mathcal{S}_G$ of (spanning) subgraphs of…
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
A graph $G$ is said to be determined by its generalized spectrum (DGS for short) if for any graph $H$, $H$ and $G$ are cospectral with cospectral complements implies that $H$ is isomorphic to $G$. It turns out that whether a graph $G$ is…
We introduce some determinantal ideals of the generalized Laplacian matrix associated to a digraph G, that we call critical ideals of G. Critical ideals generalize the critical group and the characteristic polynomials of the adjacency and…
For a graph $G=(V,E)$, a set $S \subseteq V$ is a $[1,2]$-set if it is a dominating set for $G$ and each vertex $v \in V \setminus S$ is dominated by at most two vertices of $S$, i.e. $1 \leq \vert N(v) \cap S \vert \leq 2$. Moreover a set…
In this paper, we introduce a generalization of corona of graphs. This construction generalizes the generalized corona of graphs (consequently, the corona of graphs), the cluster of graphs, the corona-vertex subdivision graph of graphs and…
We prove the existence of infinite classes of cyclic G-decompositions of the complete multipartite graph, G being a caterpillar, a hairy cycle or a cycle. All the results are obtained by the construction of d-divisible $\alpha$-labelings of…
A graph $G$ is called well-covered if all maximal independent sets of vertices have the same cardinality. A well-covered graph $G$ is called uniformly well-covered if there is a partition of the set of vertices of $G$ such that each maximal…
We consider undirected simple finite graphs. The sets of vertices and edges of a graph $G$ are denoted by $V(G)$ and $E(G)$, respectively. For a graph $G$, we denote by $\delta(G)$ and $\eta(G)$ the least degree of a vertex of $G$ and the…
We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an expanding subgraph of G. Our results imply that if one of these…
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the…
The dominating graph of a graph G is a graph whose vertices correspond to the dominating sets of G and two vertices are adjacent whenever their corresponding dominating sets differ in exactly one vertex. Studying properties of dominating…