Relations Between Vertex$–$Edge Degree Based Topological Indices and $M_{ve}$-Polynomial of $r-$Regular Simple Graph
DOI:
https://doi.org/10.29020/nybg.ejpam.v16i2.4698Keywords:
Mve-polynomial, Rooted Graph, $M_{ve}-$indices, $M_{ve}-$polynomials, 2$-$ary treeAbstract
One of the more exciting polynomials among the newly presented graph algebraic polynomials is the $M-$Polynomial, which is a standard method for calculating degree$-$based topological indices. In this paper, we define the $M_{ve}-$polynomials based on vertex$–$edge degree and derive various vertex$–$edge degree based topological indices from them. Thus, for any graph, we provide some relationships between vertex$–$edge degree topological indices. Also, we discuss the general $M_{ve}-$polynomial of $r-$regular simple graph. Finally, we computed the $M_{ve}-$polynomial of the $2-$ary tree graph.
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