Labelling of Cactus Graphs

Abstract

Communication network signal interference can be modelled using distance labelling where the labels assigned to each vertex depend on the distance between vertices and the strength of the network signal. This paper assumes three levels of signal interference within a graph, . In the graph, if the distance between any two vertices, ,and is 1 i.e., then the difference of their labels must be at least i.e., . Similarly,if , then and if , then . The -labelling number of is the smallest positive integer such that has an -labelling with as the maximum label. This paper presents a general -value for paths, bipartite graphs, complete graphs, cycles as well as Cactus Graphs that is d-dependent for any .