Related papers: Generalized splines on arbitrary graphs
Let $p\ge 3$ be a prime. A generalised multi-edge spinal group is a subgroup of the automorphism group of a regular $p$-adic rooted tree T that is generated by one rooted automorphism and $p$ families of directed automorphisms, each family…
Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total…
Fitch graphs $G=(X,E)$ are di-graphs that are explained by $\{\otimes,1\}$-edge-labeled rooted trees with leaf set $X$: there is an arc $xy\in E$ if and only if the unique path in $T$ that connects the least common ancestor…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
Spectral characterization of graphs is an important topic in spectral graph theory, which has received a lot of attention from researchers in recent years. It is generally very hard to show a given graph to be determined by its spectrum.…
An antimagic labeling of a graph $G$ is a one-to-one correspondence between the edge set $E(G)$ and $\lbrace 1,2,...,|E(G)|\rbrace$ in which the sum of the edge labels incident on the distinct vertices are distinct. Let…
In this paper we give a new generalization of token graphs. Given two integers $1\leq m \leq k$ and a graph $G$ we define the generalized token graph of the graph $G$, to be the graph $F_k^m(G)$ whose vertices correspond to configurations…
A graph $\Gamma$ is called $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of $G$-symmetric graphs $\Gamma$ with $V(\Gamma)$ admitting…
The notion of a generalized scale emerged in recent joint work with Afsar-Brownlowe-Larsen on equilibrium states on C*-algebras of right LCM monoids, where it features as the key datum for the dynamics under investigation. This work…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
A total weighting of a graph $G$ is a mapping $f$ which assigns to each element $z \in V(G) \cup E(G)$ a real number $f(z)$ as its weight. The vertex sum of $v$ with respect to $f$ is $\phi_f(v)=\sum_{e \in E(v)}f(e)+f(v)$. A total…
Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious labelings \cite{Hovey}. If $A$ is an Abelian group, then a labeling $f \colon V (G) \rightarrow A$ of the vertices of some graph $G$ induces an edge…
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…
Let R be a commutative ring with unity, M be an unitary R-module and {\Gamma} be a simple graph. This research article is an interplay of combinatorial and algebraic properties of M . We show a combinatorial object completely determines an…
We introduce a notion of generalized homogeneous derivations on graded rings as a natural extension of the homogeneous derivations defined by Kanunnikov. We then define gr-generalized derivations, which preserve the degrees of homogeneous…
We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does…
In this paper we continue the study of prime graphs of finite solvable groups. The prime graph, or Gruenberg-Kegel graph, of a finite group G has vertices consisting of the prime divisors of the order of G and an edge from primes p to q if…
For a zero-relation algebra over a field $\mathcal K$, Crawley-Boevey introduced the concept of a tree module and provided a combinatorial description of a basis for the space of homomorphisms between two tree modules--the basis elements…
A {\it universal labeling} of a graph $G$ is a labeling of the edge set in $G$ such that in every orientation $\ell$ of $G$ for every two adjacent vertices $v$ and $u$, the sum of incoming edges of $v$ and $u$ in the oriented graph are…
A total prime labeling of a graph of order $n$ is an extension of a prime labeling in which we distinctly label the vertices and edges. The goal of the labeling is for adjacent vertex labels to be relatively prime, and for each vertex of…