Abstract |
: Let G = (V,E) be considered as a simple, undirected and connected graph with a set of vertices V and a set of edges E., according to Griggs and Yeh (2004) is defined as follows. If an -labeling of graph G is a function such that whenever the distance between u and v is i apart for then we denote as the minimum span of any such labeling of G.
Application of this labeling is a radio channel assignment problem as well as to assign. codes in computer network , i.e. to assign integer channels to transmitter network with distant restriction such that some interference levels between adjacent transmitters can be avoided and the label span is minimized.
In this research, the network then is represented by graph, such that all stations are vertices and two vertices are adjacent if the corresponding stations can hear each other. Hence, two stations are at distance two, if they are outside the hearing range of each other but can be received by the same destination station. For one station, to avoid hidden terminal interference with the adjacent station that send message, we need a different codes, i.e. . Hence, two adjacent stations are allowed to have the same code, meaning . Here we have the cases.
If we require a distinct codes for any two adjacent stations, i.e. then to avoid a direct interference, as well as to avoid hidden terminal interference, we will require a larger code differences between any two stations at distance two (which cannot hear each other. but can both received by the same stations), i.e., Thus, we have the and cases. |