We call a simple graph G a linear N-graph if its ordinary (vertex) chromatic number equals to the linear chromatic number of its neighborhood complex N(G). We prove that the linearity is preserved under taking joins and multiplication of vertices, and give a complete characterization of linear N-trees.
Taylan, Demet and Baser, Gulnur
Rose-Hulman Undergraduate Mathematics Journal: Vol. 8:
1, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol8/iss1/9