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 $T_{3, n}$.