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A Water ATM is a computerized water peddling machine that give out pure drinking water when a coin, note, card is placed into it. The key objective of this paper is to maintain the Water ATMs and choice of sites for the Water ATMs on basis of external/Internal factors of the site so that maximum number of people gains the benefits. It comes across the pure drinking water supplies at public places for citizens/visitors.
Municipality water supply is irregular in most of the cities. Slowly growing the gap between demand and supply of water. Frequent failures of government water planned create very bad condition for people depend on it. People living in hilly area and upper slopes do not have piped water supply.
Graph theory has numerous applications in Computer Science. One of the NP complete problems of Graph theory is Vertex Cover problem and Graph coloring problem.
Vertex Cover
It is a subset of vertices of undirected graph (G), so that each edge (u,v) of the G, either u or v is in vertex cover and it includes all the edges of the G.
Minimum Vertex Cover defines the least possible number of vertices that includes all the edges of the G.
Graph Coloring Problem
It is a grouping of vertices such that no two nearby vertices have the identical color. Coloring the graph with least number of colors is also of great importance as it effects how well a problem can be resolved.
Various papers of different researchers used only External factors to select the location Water ATMs. This is no any method used by any author for the site selection. These are no such works on the maintenance of Water ATMs.
In this paper, the authors considered both the internal factors as well external factors of the site selection. Example: Amount of water, Superiority of water, Remoteness of water supply source, Landscape of city and its surroundings, Altitude of source of water supply etc. also important for section of locations for placing Water ATMs. Here authors used Minimum Vertex cover method to find out the locations and algorithm is designed to find the optimal locations. In this paper authors have used Vertex Colouring technique to perform the maintenance of Water ATMs.
Background
Zhang R. et al. (2020) discussed on chromatic polynomials of hypergraph. The idea of chromatic polynomial of a hypergraph is a usualdelay of chromatic polynomial of a graph. They have stressed on presenting some significant open problems on chromatic polynomials of hypergraph.
Sreekumar et al. (2021) analyses the semi-regular bipartite graphs, its subclass graph, SM sum graphs, SM balancing graphs all are automorphism group of a class. The relationship between the graphs is also established. By using Nauty algorithm, they find out the size of the graph.
Charbit et al. (2021) studied the edge clique cover number of graphs with independence number two, which are necessarily claw-free. They gave the first known proof of a linear bound in n for ecc(𝐺) for such graphs, improving upon the bound of 𝑂(𝑛4∕3log1∕3 𝑛) .More precisely they proved that ecc(𝐺) is at most the minimum of 𝑛+𝛿(𝐺) and 2𝑛−Ω(√𝑛log 𝑛),where 𝛿(𝐺) is the minimum degree of G.
Foucaud et al. (2017) proved two conjectures for the class of line graphs. Both bounds are tight for this class, in the sense that there are infinitely many connected line graphs for which equality holds in the bounds.
Mei-Mei et al. (2020) considered the 2-good-neighbor diagnosability of some general k-regular k connected graphs G under the PMC model and the MM* model. The key result t PMC 2 (G) = tMM∗ 2 (G) = g(k − 1) − 1 with some suitable conditions is obtained, where g is the girth of G.