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 total graph is built by joining the to its line means of incidences. We introduce a similar construction for signed graphs. Under two defnitions graph, we defne corresponding and show that it stable under switching. consider balance, frustration index number, largesteigenvalue. In regular case compute spectrum adjacency matrix spectra certain compositions, determine some with exactly main e...

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...

Signed link prediction in social networks aims to reveal the underlying relationships (i.e., links) among users nodes) given their existing positive and negative interactions observed. Most of prior efforts are devoted learning node embeddings with graph neural (GNNs), which preserve signed network topology by message-passing along edges facilitate downstream task. Nevertheless, graph-based app...

This paper surveys recent development of concepts related to coloring signed graphs. Various approaches are presented and discussed.

This paper studies learning meaningful node representations for signed graphs, where both positive and negative links exist. problem has been widely studied by meticulously designing expressive graph neural networks, as well capturing the structural information of through traditional structure decomposition methods, e.g., spectral theory. In this paper, we propose a novel representation framewo...

Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...