Total edge domination polynomials of Tadpole \(T_{3, n}\)

Abstract

Tadpole graph \(T_{3, n}\) is a special graph obtained by appending a cycle \(C_3\) to a path \(P_n\). In this paper we present the Total edge domination polynomial of \(T_{3, n}, D_{t e}\left(T_{3, n}, x\right)=\sum_{i=\gamma_i^{\prime}\left(T_{3, n}\right)}^{n+3} d_{t e}\left(T_{3, n}, i\right) x^i\). Also we derive some properties of Total Edge domination polynomials of \(T_{3, n}\).