In this note, we show that automata theory is a suitable tool for analyzing monopoly-forcing processes. Also, we present the notion of mono-forcing automata by using the monopoly-forcing set for graphs. Moreover, we prove that mono-forcing automata accept more languages than zero-forcing finite automata also, we show that all results in zero-forcing finite automata for complete graphs are established for mono-forcing automata. We examine and deliberate on the language associated with mono-forcing automata for certain specified graphs. Also, we present the style of words that can be recognized with mono-forcing automata. Additionally, we delineate the types of words identifiable by mono-forcing automata. We also describe the configuration of graphs from which mono-forcing automata emerge, generating specific languages. Several examples are provided to elucidate these concepts.

The current study aims to establish a connection between graphs and automata theory, which apparently demonstrate di erent mathematical structures. Through searching out some properties of one of these structures, we try to  nd some new properties of the other structure as well. This will result in obtaining some unknown properties. At  rst, a novel automaton called zero-forcing (Z-F)  nite automata is de ned according to the notion of a zero-forcing set of a graph. It is shown that for a given graph and for some zero forcing sets, various Z-F- nite automata will be obtained. In addition, the language and the closure properties of Z-F- nite automata, in particular; union, connection, and serial connection are studied. Moreover, considering some properties of graphs such as the closed trail, connected and complete; some new features for Z-F- nite automata are presented. Further, it is shown that there is not any  nite graph such that f be a part of the language of its Z-F- nite automata. Actually, it is proved that for every given graph, the Z-F- nite automata of it does not show any closed trail containing all edges for every zero forcing set, but if the graph G has been a closed trail containing all edges, then the Z-F- nite automata of it has a weak closed trail containing all edges. Some examples are also given to clarify these new notions.

Introduction: According to association of daytime symptoms, nocturnal enuresis is divided into 2subgroups: mono-symptomatic (MNE) and nonmono symptomatic (NMNE) forms.This study was conducted to review clinical and ultrasonography findings in different subtypes of enuresis and compare organic and functional pathologies of lower urinary tract in children with MNE with those who have NMNE.Methods: During 3-year period neurologically normal children with enuresis who referred nephrology clinic were enrolled study. Urinalysis, urine culture, and ultrasonography were done forall. Voiding CystoUreteroGraphy (VCUG) was used to evaluate anatomy of lower urinary tract and Urodynamic Studies (UDS) were done to assess bladder function.Results: Hundred and eleven children enrolled study (60 boys and 51 girls). Forty-three (38.8%) with MNE and 68 (61.2%) with NMNE, aged 5 to 17 years. Constipation, encopresis, and urge incontinence were significantly more frequent in patients with NMNE + daytime incontinence (P<.05). Increased of bladder wall thickness and irregularity of bladder wall were the most common findings (P>.05). One patient with MNE and 9 with NMNE + daytime incontinence had vesicoureteral reflux (P=.02). Evidences of bladder dysfunction were noted in about half of patients who underwent UDS, with higher prevalence in cases with NMNE +daytime urinary incontinence (P>.05).Conclusions: Bowel symptoms and urological abnormalities of lower urinary tract are significantly more prevalent in cases with NMNE who have daytime incontinence. We recommend VCUG in patients with NMNE who have daytime incontinence.

Let be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of is a set of disjoint edges which covers all vertices of . The anti-forcing number of is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by . For every , the th power of , denoted by , is a graph with the same vertex set as such that two vertices are adjacent in if and only if their distance is at most in . In this paper, we study the anti-forcing number of the powers of some graphs.

In this paper, for a given graph, G, some domination parameters and the forcing domination number of the graph, M (G), obtained from G arising in Mycielski's construction, are studied.