Path Concatenation

Topics: Path - Graph Theory

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(definition)

The concatenation of two paths $W_1=\left\{v_0,e_1,v_1,\dots ,e_k,v_k\right\}$ and $W_2=\left\{v_k,e_{k+1},v_{k+1},\dots ,e_n,v_n\right\}$ is the set:

$$W_1\circ W_2=\left\{v_0,e_1,v_1\dots ,e_k,v_k,e_{k+1},v_{k+1},\dots ,e_n,v_n\right\}$$

Notice that the final vertex in $W_1$ is the initial one in $W_2$.