The locating-chromatic number of a graph combines two concepts, namely coloring vertices and partition dimension graph. is the smallest k such that G has locating k-coloring, denoted by χL(G). This article proposes procedure for obtaining an origami its subdivision (one vertex on outer edge) through theorems with proofs.

In 1998, Pandu Rangan et al. proved that locating the g-centroid for an arbitrary graph is -hard by reducing the problem of finding the maximum clique size of a graph to the g-centroid location problem. They have also given an efficient polynomial time algorithm for locating the g-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present an O(nm) tim...

The paper generalizes the notion of locating-chromatic number of a graph such that it can be applied to disconnected graphs as well. In this sense, not all the graphs will have finite locating-chromatic numbers. We derive conditions under which a graph has a finite locating-chromatic number. In particular, we determine the locatingchromatic number of a uniform linear forest, namely a disjoint u...

We study the problems Locating-Dominating Set and Metric Dimension, which consist in determining a minimum-size set of vertices that distinguishes the vertices of a graph using either neighbourhoods or distances. We consider these problems when restricted to interval graphs and permutation graphs. We prove that both decision problems are NP-complete, even for graphs that are at the same time in...

bandwidth labelling is a well known research area in graph theory. we provide a new proof that the bandwidth of mobius ladder is 4, if it is not a $k_{4}$, and investigate the bandwidth of a wider class of mobius graphs of even strips.

In this paper, we are dealing with the study of locating chromatic number Möbius-ladders. We prove that Möbius-ladders Mn n even has 4 if n≠6 and 6 n=6.