Question

What is the degree sequence of the given HyperGraph, in non-increasing order.
V = {v1,v2,v3,v4,v5,v6} E = {{v1,v4,v5} {v2,v3,v4,v5} {v2} {v1} {v1,v6}}

Answer 1

Correct option is B. 3,2,2,2,1,1
The degree sequence of a hypergraph is the list of vertex degrees in non-increasing order.

For, $$E=\{e_1=\{v_1,v_2,v_3\},e_2=\{v_2,v_3\},e_3=\{v_3,v_5,v_6\},e_4=\{v_4\}\}$$

The degree sequence is,

$$[d_{ij}]_{i=1}^7=d_1\geq d_7=3,2,1,1,1,1,0$$

Similarly for $$V=\{v_1,v_2,v_3,v_4,v_5,v_6\}$$

$$E=\{v_1,v_4,v_5\},\{v_2,v_3,v_4,v_5\},\{v_2\},\{v_1\}\{v_1,v_6\}\}$$

The degree of $$V_1.V_2.V_3.V_4,V_5,V_6$$ is,

$$3,2,1,2,2,1$$

Option $$\textbf B$$ is correct