Volume 68 | Issue 4 | Year 2022 | Article Id. IJMTT-V68I4P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I4P508

Received | Revised | Accepted |
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13 Mar 2022 | 15 Apr 2022 | 19 Apr 2022 |

In a graph G = (V, E), a vertex v∈V, ve-dominates every edge incident to it as well as every edge adjacent to these incident edges. The vertex-edge degree of a vertex v, is denoted by d<sup>ve</sup>(v) and is the number of edges ve-dominated by v. In this paper, we introduce the vertex-edge eccentric connectivity index of a graph G, denoted by ξ^{c}_{vee}(G) and is equal to the sum of the product of the connectivity and ve-degree of the vertices of G. We calculate the vertex-edge eccentric connectivity index of some wheel related graphs and windmill graphs. Finally, we obtain some upper and lower bounds on ξ^{c}_{vee}(G).

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Shiladhar Pawar, "On Vertex-Edge Eccentric Connectivity Index of Wheel related and
Windmill Graphs," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 68, no. 4, pp. 43-51, 2022. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V68I4P508