a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

A signed graph (or sigraph in short) is an ordered pair S = (Su, σ), where Su is a graph G = (V,E), called the underlying graph of S and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}, called the signature of S. The ×-line sigraph of S denoted by L×(S) is a sigraph defined on the line graph L(S u) of the graph Su by assigning to each edge ef of L(Su), the product of si...

a emph{signed graph} (or, in short, emph{sigraph}) $s=(s^u,sigma)$ consists of an underlying graph $s^u :=g=(v,e)$ and a function $sigma:e(s^u)longrightarrow {+,-}$, called the signature of $s$. a emph{marking} of $s$ is a function $mu:v(s)longrightarrow {+,-}$. the emph{canonical marking} of a signed graph $s$, denoted $mu_sigma$, is given as $$mu_sigma(v) := prod_{vwin e(s)}sigma(vw).$$the li...

Security of a network is important to all organizations, personal computer users, and the military. With the invention of the Internet, major concern is about the security and the history of security allows a better understanding of the emergence of security technology. One of the ways to secure businesses from the Internet is through firewalls and encryption mechanisms. A network can be design...

A signedgraph (or sigraph in short) S is a graph G in which each edge x carries a value [Formula: see text] called its sign   denoted specially as [Formula: see text]. Given a sigraph S,  H = L(S)   called the line sigraph of S is that sigraph in which edges of S are represented as vertices, two of these vertices are defined to be adjacent whenever the corresponding edges in S have a vertex in ...

Bacillus subtilis transports β-glucosides such as salicin by a dedicated phosphotransferase system (PTS). The expression of the β-glucoside permease BglP is induced in the presence of the substrate salicin, and this induction requires the binding of the antiterminator protein LicT to a specific RNA target in the 5' region of the bglP mRNA to prevent the formation of a transcription terminator. ...

The Bacillus subtilis sacY and sacT genes encode antiterminator proteins, similar to the Escherichia coli bglG gene product and required for transcription of sucrose metabolism genes. A Tn10 insertion into bglP (formerly sytA) has been previously identified as restoring sucrose utilization to a strain with deletions of both sacY and sacT. The nucleotide sequence of bglP showed a high degree of ...

Background: Exercise training and crocin, as a herbal antioxidant, help improve metabolism insulin sensitivity in type 2 diabetes mellitus (T2D). AMP-activated protein kinase (AMPK) nuclear respiratory factor 1 (NRF1) involve the mitochondrial biogenesis pathway control. Objective: This study aimed to investigate effects of high-intensity interval (HIIT), low intensity continued (LICT) combinat...