Discrete Mathematics Answers - Assignment

Added on - 21 Feb 2021

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Discrete Mathematics for IT
TABLE OF CONTENTINTRODUCTION...........................................................................................................................1PROBLEM DEFINITION..............................................................................................................1REAL WORLD APPLICATION...................................................................................................3PROBLEM SOLUTION.................................................................................................................3POSSIBLE ALGORITHM.............................................................................................................7CONCLUSION...............................................................................................................................8SHORT STATEMENT...................................................................................................................8REFERENCES.............................................................................................................................10
INTRODUCTIONMathematical investigation is defined as the exploration and analysis of mathematicalsituations through an open-handed approach. The discrete graphical structures are considered asvery significant for modelling the interconnection between various objects. The analysis ofgraphical tools is very helpful in solving real life applications and issues (Sheng, Li and Gutin,2017). One such example of mathematical problem is construction of Euler circuit which is usedto solve variety of problems like mail and carriers problem and Konigsberg bridge problem. Thereport will investigate the Euler circuit and its construction and how this problem find its place inthe real world applications. It will also analyse the most effective solution and algorithms usedfor the problem.PROBLEM DEFINITIONIn a graph Euler path is defined as the trail in which each edge is visited exactly at once.On the other hand Eulerian circuit is known as the Eulerian path which initiate and terminate onsame vertex (Lamagna, 2019). For the problem description it can be stated that for a given graphit is possible to construct or develop a path which visit each edge of the graph exactly at oncewith its initial and ending points. Let us consider an example of graph consisting of Euler pathand circuit.For instance in the above graph BBADCDEBC is one of the Euler path in which each and everyedge is traversed only at once. However the nodes or the vertex can be repeated. The starting andending point of this path are B and C respectively and thus they are different. Hence it is calledEuler path and not Euler circuit. Similarly in the graph another Euler path which is observed isCDCBBADEB.1
The Euler circuit which is constructed in the given graph is CDCBBADEBC. In this circuitedges are traversed only at once but the initial and terminating vertex is same in the path. Due tothis reason it is known as Euler circuit.A single graph can have multiple Euler's path and circuit. The above graph has another circuit asCDEBBADC. There are some specific criterion for having or constructing a Euler circuit. Forexample if a graph (G) has an Euler circuit (C) then it must satisfy specific conditions. For eachof the vertex (v) each edge has endpoint which are demonstrated only at once. In addition to thiswhen G has Euler circuit, then number of time v enters and leaves the circuit is same. For theEulerian circuits vertex v is even or multiple of two because degree of v is (2*s) where s is thenumber of times Euler circuit enters vertex which is also equal to number of times it leaves2
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