Question

A graph G has the degree of each vertex is ≥ 3 say,  deg(V) ≥ 3 ∀ V ∈ G such that 3|V| ≤ 2|E| and 3|R| ≤ 2|E|, then the graph is said to be ________ (R denotes region in the graph)

(a) Planner graph

(b) Polyhedral graph

(c) Homomorphic graph

(d) Isomorphic graph

The question was asked at a job interview.

This interesting question is from Isomorphism in Graphs topic in chapter Graphs of Discrete Mathematics

Answer 1

The correct choice is (b) Polyhedral graph

The best I can explain: A simple connected planar graph is called a polyhedral graph if the degree of each vertex is(V) ≥ 3 such that deg(V) ≥ 3 ∀ V ∈ G and two conditions must satisfy i) 3|V| ≤ 2|E| and ii) 3|R| ≤ 2|E|.