A circular r-coloring of a signed graph (G, σ) is to assign points of a circle of circumference r,
r≥ 2, to the vertices of G such that vertices connected by a positive edge are at circular …

In this paper, the concept of circular rr‐flow in a mono‐directed signed graph (G, σ) (G,σ) is
introduced. That is a pair (D, f) (D,f), where DD is an orientation on GG and f: E (G)→(− r, r) …

We say that a signed graph is kk‐critical if it is not kk‐colorable but every one of its proper
subgraphs is kk‐colorable. Using the definition of colorability due to Naserasr, Wang, and …

A homomorphism of a signed graph (G, σ) (G,σ) to (H, π) (H,π) is a mapping of vertices and
edges of GG to (respectively) vertices and edges of HH such that adjacencies, incidences …

Given a signed graph (G, σ) and a positive real number r, if there exists a vertex mapping c:
V (G)→[0, r) satisfying that for every positive edge wx, 1≤| c (w)− c (x)|≤ r− 1 and for every …

A signed graph is a graph G together with an assignment sigma: E (G)->{+,-}. Graph coloring
and homomorphism are two of the central problems in graph theory, and those notions and …