An Algebraic Representation of Graphs and Applications to Graph Enumeration

Figure 4

(a) An isolated vertex represented by 1∈𝖲(𝑉). (b) A 2-vertex tree represented by 𝑅_1,2∈𝖲(𝑉)^⊗2. (c) A triangle represented by 𝑅_1,2⋅𝑅_1,3⋅𝑅_2,3∈𝖲(𝑉)^⊗3.

(a)

(b)

(c)