Incidence Coloring Numbers of Two Classes of Planar Graphs
Zhang Li, Dong-Ling Chen · Journal of Tongji University · 2008
A wheel W_(r+1)(r≥3) is a graph obtained from a cycle of order r by adding a new vertex and joining the new vertex to all the vertices on the cycle. The new edges between the new vertex and the vertices on the cycle are called spoke edges,the edges on the cycle are called rim edges.A flower graph F_(r,m,n)(r≥3,m≥1,n≥2m+1) is a graph obtained from W_(r+1) by inserting m-1 new vertices in every spoke edge and n-2m-1 new vertices in every rim edge.The planar graph Q_n(n≥3) called a prism is defined by Q_n=G(V,E),V={u_1,u_2,…,u_n}∪{v_1,v_2,…,v_n} and E={u_iu_(i+1), v_iv_(i+1),u_iv_i,u_iv_(i+1)|i=1,2,…,n},where u_(n+1)=u_1,v_(n+1)=v_1.Based on incidence coloring methods of F_(r,m,n)(r≥3,m≥1,n≥2m+1) and Q_n(n≥3),the incidence coloring numbers of them are determined.