Topological Indices on Model Graph Structure of Alveoli in Human Lungs
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Alveoli are hollow cavitites within the human body. In the present study, alveoli of human lungs are considered which are healthy and also when a ected by emphysema loss of elasticity resulting in breathing diculties. It is interesting to apply graph theory with a view to test and predict the status of alveoli in both healthy lungs and when a ected. The model developed can be used for further advancement in the medical eld for any diagnosis with respect to the lung diseases. The purpose of this paper is to investigation of Alveoli in Human lungs using concept of Topological indices. Here we have attempted to use double graphs by considering the alveoli as a connected graph. Topological indices are determined for healthy and ruptured alveoli by using graph operator called double graphs. PI and Szeged indices have been found for a healthy alveoli as was modelled earlier. Four graph operators namely S(G) , R(G) , Q(G) and L(G) are obtained and their respective PI and Szeged indices are studied. Finally, a comparative study is made for all the operators with respect to the a ected alveoli in order to better facilitate the modeling to help detect the defects early.
Abstract
Alveoli are hollow cavitites within the human body. In the present study, alveoli of human lungs are considered which are healthy and also when a ected by emphysema loss of elasticity resulting in breathing diculties. It is interesting to apply graph theory with a view to test and predict the status of alveoli in both healthy lungs and when a ected. The model developed can be used for further advancement in the medical eld for any diagnosis with respect to the lung diseases. The purpose of this paper is to investigation of Alveoli in Human lungs using concept of Topological indices. Here we have attempted to use double graphs by considering the alveoli as a connected graph. Topological indices are determined for healthy and ruptured alveoli by using graph operator called double graphs. PI and Szeged indices have been found for a healthy alveoli as was modelled earlier. Four graph operators namely S(G) , R(G) , Q(G) and L(G) are obtained and their respective PI and Szeged indices are studied. Finally, a comparative study is made for all the operators with respect to the a ected alveoli in order to better facilitate the modeling to help detect the defects early.
참고문헌 (15)
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