# Application of graph theory in domination of graphs

If G has a Hamiltonian Cycle then the same ordering of nodes is a Hamiltonian path of G0 if we split up v into v0 and v The Boolean formula will usually be given in CNF conjunctive normal form , which is a conjunction of multiple clauses, where each clause is a disjunction of literals variables or negation of variables. Efficient algorithms for Roman domination on some classes of graphs. A Hamiltonian cycle is a Hamiltonian path plus an additional edge connecting the free ends of the path. The challenge is to start at the city c 1 and to then travel through each city exactly once returning at the end to c 1 and using only open roads. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamiltonian paths. In the most extreme case a single Hamiltonian cycle of su cient size can actually protect all single span failures in the network as all spans will either be an on cycle span or a straddling span for that cycle.

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## Applications of Graph Theory

This problem is an outgrowth of the well-known four-colour map problem , which asks whether the countries on every map can be coloured by using just four colours in such a way that countries sharing an edge have different colours. Retrieved 27 May Computer science Theory of computation Numerical analysis Optimization Computer algebra. List structures are often preferred for sparse graphs as they have smaller memory requirements. Graphs are used to represent data organization. A dominating set may or may not be an independent set.

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### Graph Theory Applications - javatpoint

Finding maximal induced subgraphs of a certain kind is also often NP-complete. Social Sciences Graph theory is also used in sociology. Algorithm design Analysis of algorithms Algorithmic efficiency Randomized algorithm Computational geometry. Still another such problem, the minor containment problem, is to find a fixed graph as a minor of a given graph.

## Dominating set

Description: Furthermore, there is a simple algorithm that maps a dominating set to a set cover of the same size and vice versa. Equivalently, it is the size of the smallest maximal independent set. Control S. Concurrent computing Parallel computing Distributed computing Multithreading Multiprocessing. In these applications, graphs are ordered by specificity, meaning that more constrained graphs—which are more specific and thus contain a greater amount of information—are subsumed by those that are more general.

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Date: 18.12.2019
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