Let Γ be a G-symmetric graph whose vertex set admits a nontrivial G-invariant partition B with block size v. Let ΓB be the quotient graph of Γ relative to B and Γ [B,C] the bipartite subgraph of Γ induced by adjacent blocks B,C of B. In this paper we study such graphs for which ΓB is connected, (G,2)-arc transitive and is almost covered by Γ in the sense that Γ [B,C] is a matching of v−1≥2 edge...

We study the problem of scheduling groups of tasks with precedence constraints on three dedicated processors. Each task requires a speci3ed set of processors. Up to three precedence constraints are considered among groups of tasks requiring the same set of processors. The objective of the problem is to 3nd a nonpreemptive schedule which minimizes the maximum completion time (makespan). This sch...

The directed power graph G?(G) of a group G is the simple digraph with vertex set such that x?y if y x. G, denoted by G(G), underlying graph. In this paper, for groups and H, following proved. If has no quasicyclic subgroup Cp? which trivial intersection every cyclic K K??Cp?, then G(G)?G(H) implies G?(G)?G?(H). particular, any two torsion-free having isomorphic graphs have graphs.

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory robust theory. By challenging the classical Laplacian, propose a new convolution operator that is provably in domain and incorporated GCN architecture improve expressiv...

The aim of this paper is to introduce power idealization filter topologies with respect to filter topologies and power ideals of lattice implication algebras, and to investigate some properties of power idealization filter topological spaces and their quotient spaces.

We introduce and give a complete description of a new graph to be used for DNA sequencing questions. This graph has the advantage over the classical de Bruijn graph that it fully accounts for the double stranded nature of DNA, rather than dealing with single strands. Technically, our graph may be thought of as the quotient of the de Bruijn graph under the natural involution of sending a DNA str...

The purpose of this note is to define a graph whose vertex set finite group G $G$ , edge contained in that the commuting and contains enhanced power . We call deep Two elements are joined if only their inverse images every central extension commute. give conditions for be equal either graph, show automorphisms act as graph.

Consider the following general question: if we can solve Maximum Matching in (quasi) linear time on a graph class C , does same hold true for of graphs that be modularly decomposed into ? What makes latter question difficult is problem not preserved by quotient, thereby making to exploit structural properties quotient subgraphs modular decomposition. So far, are only aware recent framework (Cou...

We investigate graphs and hypergraphs that have (relaxed) product structures. In the class of graphs, we discuss in detail RSP-relations, a relaxation of relations fulfilling the square property and therefore of the product relation σ, that identifies the copies of the prime factors of a graph w.r.t. the Cartesian product. For K2,3-free graphs finest RSP-relations can be computed in polynomial-...