فهرست نشریات علمی دسترسی آزاد ایران

In this paper, we introduced the concept of edge geodetic sequences in graph and its generating function. Some general properties satisfied by this concept are studied. It is shown that for every generating function$$ G(x)=\sum_{i=1}^{\infty} {a}^{i-1}{x^{i-1}} \quad a\in N-\left\lbrace 1\right\rbrace,$$there exists a recurrence graph $G$ with edge geodetic decomposition $\pi=\{G_{1},G_{2},\ldots ,G_{n}\ldots\}$.