Exploring Novel Edge Connectivity in Graph Theory and its Impact on Eulerian Line Graphs

Rajeshri Prajapati, Amit Parikh, Pradeep Jha

Abstract: This study introduces a groundbreaking concept in graph theory: Edge Connectivity, which aids in predicting the Eulerity of a line graph without the need to draw the line graph L(G)of a connected graph G. The paper not only delineates this novel concept but also discusses its salient features and applications, emphasizing its importance in graph theory. Through rigorous theoretical analysis, the study demonstrates the potential of Edge Connectivity in simplifying and enhancing the understanding of complex graph relationships, thereby opening new avenues for research in this field.

Keywords: Line Graph, Edge Connectivity, Dual Graph, Link Vertex, Eulerian Graphs, Graph Theory Applications

How to Cite?: Rajeshri Prajapati, Amit Parikh, Pradeep Jha, "Exploring Novel Edge Connectivity in Graph Theory and its Impact on Eulerian Line Graphs", Volume 12 Issue 11, November 2023, International Journal of Science and Research (IJSR), Pages: 1515-1519, https://www.ijsr.net/getabstract.php?paperid=SR231120155230, DOI: https://dx.doi.org/10.21275/SR231120155230