Given a pair (X, σ) consisting of a finite tree X and its vertex self-map σ one can construct the corresponding Markov graph Γ(X, σ) which is a digraph that encodes σ-covering relation between edges in X. M-graphs are ...

Let G be a graph with the eigenvalues λ1(G) >· · · > λn(G). The largest eigenvalue of G, λ1(G), is called the spectral radius of G. Let β(G) = ∆(G) − λ1(G), where ∆(G) is the maximum degree of vertices of G. It is known ...

Let Zn be the finite commutative ring of residue classes modulo n with identity and Γ(Zn) be its zero-divisor graph. In this paper, we investigate some properties of nilradical graph, denoted by N(Zn) and non-nilradical ...

For a commutative ring R and an ideal I of R, the ideal-based zero-divisor graph is the undirected graph ΓI (R) with vertices {x ∈ R−I : xy ∈ I for some y ∈ R−I}, where distinct vertices x and y are adjacent if and only ...

Let S be a pomonoid. In this paper, Pos-S, the category of S-posets and S-poset maps, is considered. One of the main aims of this paper is to draw attention to the notion of weak factorization systems in Pos-S. We show ...