Related papers: Zero-divisor graphs of lower dismantlable lattices…
The zero-divisor graph $\Gamma(R)$ of an associative ring $R$ is the graph whose vertices are all nonzero zero-divisors (one-sided and two-sided) of $R$, and two distinct vertices $x$ and $y$ are joined by an edge iff either $xy=0$ or…
We study lattices acting on $\mathrm{CAT}(0)$ spaces via their commensurated subgroups. To do this we introduce the notions of a graph of lattices and a complex of lattices giving graph and complex of group splittings of $\mathrm{CAT}(0)$…
We study the undirected divisibility graph in which the vertex set is a finite subset of consecutive natural numbers up to N.We derive analytical expressions for measures of the graph like degree, clustering, geodesic distance and…
This is my dissertation about digraphs ordered by pp-constructability. We study in particular smooth digraphs, i.e., digraphs without sources or sinks, tournaments and semicomplete digraphs, orientations of paths and cycles, digraphs with…
This paper proposes a novel representation of decomposable graphs based on semi-latent tree-dependent bipartite graphs. The novel representation has two main benefits. First, it enables a form of sub-clustering within maximal cliques of the…
In this paper, we study the zero divisor graph $\Gamma^m(L)$ of a multiplicative lattice L. We prove under certain conditions that for a reduced multiplicative lattice L having more than two minimal prime elements, $\Gamma^m(L)$ contains a…
The Divisibility Graph of a finite group $G$ has vertex set the set of conjugacy class lengths of non-central elements in $G$ and two vertices are connected by an edge if one divides the other. We determine the connected components of the…
Let $(A, \oplus, *, 0)$ be an MV-algebra, $(A, \odot, 0)$ be the associated commutative semigroup, and $I$ be an ideal of $A$. Define the ideal-based zero-divisor graph $\Gamma_{I}(A)$ of $A$ with respect to $I$ to be a simple graph with…
In this paper we begin the study of well-failed graphs, that is, graphs in which every maximal failed zero forcing set is a maximum failed zero forcing set, or equivalently, in which every minimal fort is a minimum fort. We characterize…
A graph in which all minimal zero forcing sets are in fact minimum size is called ``well-forced." This paper characterizes well-forced trees and presents an algorithm for determining which trees are well-forced. Additionally, we…
A distributive lattice $L$ with minimum element $0$ is called decomposable if $a$ and $b$ are not comparable elements in $L$ then there exist $\overline{a},\overline{b}\in L$ such that $a=\overline{a}\vee(a\wedge b),…
The paper systematically classifies rings based on the dominant metric dimensions (Ddim) of their associated CZDG, establishing consequential bounds for the Ddim of these compressed zero-divisor graphs. The authors investigate the interplay…
Let $S$ be an inverse semigroup with zero and let $Z(S)^\times$ be its set of non-zero divisors with respect to the natural partial order $\le $ on $S$, that is, $a \in Z(S)^\times $ if there exists $b\in S\setminus\{0\}$ with $\omega(a, b)…
Assume that $R$ is a commutative ring with nonzero identity. In this paper, we introduce and investigate zero-annihilator graph of $R$ denoted by $\mathtt{ZA}(R)$. It is the graph whose vertex set is the set of all nonzero nonunit elements…
The aim of this work is to investigate the F-index and F-coindex of the line graphs of the cycle graphs, star graphs, tadpole graphs, wheel graphs and ladder graphs using the subdivision concepts. F-index of the line graph of subdivision…
A dissociation set of a graph is a set of vertices which induces a subgraph with maximum degree less than or equal to one. The dissociation number of a graph is the maximum cardinality of its dissociation sets. In this paper, we study the…
The non-solvable graph of a finite group G is a simple graph whose vertices are the elements of G and there is an edge between x and y if and only if the subgroup generated by x and y is not solvable. The isolated vertices in the…
As in algebraic geometry, an effective divisor class on a vertex-weighted graph is called special if also its residual class is effective. We study the question, when this is true already on the level of divisors; that is, when there exists…
The correspondence between unmixed bipartite graphs and sublattices of the oolean lattice is discussed. By using this correspondence, we show the existence of squarefree quadratic initial ideals of toric ideals arising from minimal vertex…
We give new decomposition theorems for classes of graphs that can be transduced in first-order logic from classes of sparse graphs -- more precisely, from classes of bounded expansion and from nowhere dense classes. In both cases, the…