Yue Feng LIN
A connected plane graph G is called a k‖δv,f- plane graph if δv,fk.there, δv,f is the minimum value of δv and δf, δv is the minimum degree of vertices ofGand δf is the minimum degree of faces of G.We mainly study the 3‖δv,f-plane graphs.We first prove the existence of the 3‖δv,f-plane graphs with the link component number 1 by constructing them via a graph operation, and prove the uniqueness of the 3‖δv,f-plane graph with link component number not less than nullity in the sense of equivalence.Then we prove the uniqueness of 3‖δv,f-plane graph with the edge number 6 and 8 in the sense of equivalence.We also show that there are only two 3‖δv,f-plane graphs with the edge number 9 in the sense of equivalence, furthermore, they are dual.After that, we study the correlations between a connected plane graph and its medial graphs in the sense of equivalence.Finally, as applications, we prove three uniqueness conclusions of lune-free link graphs.
