mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

We study unit disk visibility graphs, where the relation between a pair of geometric entities is defined by not only obstacles, but also distance them. This particular graph class models real world scenarios more accurately compared to conventional graphs. first define and classify then show that 3-coloring problem NP-complete when model used for set line segments (which applies points) polygon...

In 2005, Exoo posed the following question. Fix $\epsilon$ with $0\leq\epsilon<1$. Let $G_\epsilon$ be graph whose vertex set is Euclidean plane, where two vertices are adjacent iff distance between them lies in closed interval $[1-\epsilon,1+\epsilon]$. What chromatic number $\chi(G_\epsilon)$ of this graph? The case $\epsilon=0$ precisely classical ``chromatic plane'' problem. a 2018 p...