for any $k in mathbb{n}$, the $k$-subdivision of graph $g$ is a simple graph $g^{frac{1}{k}}$, which is constructed by replacing each edge of $g$ with a path of length $k$. in [moharram n. iradmusa, on colorings of graph fractional powers, discrete math., (310) 2010, no. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $g$ has been introduced as a fractional power of $g$, denoted by ...

A signed graph is a pair $(G, \sigma)$, where $G$ (loops and multi edges allowed) $\sigma: E(G) \to \{+, -\}$ signature which assigns to each edge of sign. Various notions coloring graphs have been studied. In this paper, we extend circular graphs. Given \sigma)$ with no positive loop, $r$-coloring an assignment $\psi$ points circle circumference $r$ the vertices such that for every $e=uv$ $G$,...

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...