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Computation of the Resistance Distance Metric in Two Classes of DNA Network
1School of Economics and Law, Chaohu University, Chaohu, 238000, P.R. China.
Introduction:
Resistance distance, originating from electrical network theory, provides a powerful framework for characterizing the structural and topological properties of chemical graphs. The objective of this study is to compute and analyze resistance-distance metrics for two distinct classes of DNA networks, with the aim of gaining deeper insight into their underlying molecular topology.
Methods:
Each DNA network is modeled as an electrical network by replacing every edge with a unit resistor. Techniques from classical electrical network theory are employed to derive resistance distances between selected pairs of vertices. Analytical simplification and elimination principles are used to obtain closed-form expressions for these distances.
Results:
Explicit resistance distance formulas are obtained for representative vertex pairs in both classes of DNA networks. The results reveal how network topology, connectivity patterns, and structural variations influence effective resistance, highlighting clear distinctions between the two DNA network classes.
Discussion:
The findings demonstrate that resistance distance effectively captures both local and global structural features of DNA networks. These results enhance the understanding of how topological complexity impacts electrical and structural behavior in molecular graphs, offering meaningful interpretations within chemical graph theory.
Conclusion:
This study provides a comprehensive resistance distance-based characterization of two classes of DNA networks. The results contribute to the broader understanding of structural flexibility and stability in molecular systems and suggest potential applications in chemical and biological engineering. MSC subject classification: 05C50, 05C90.
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