In this paper, we present characterizations of pairs of graphs whose join graphs are 2-minimally nonouterplanar. In addition, we present a characterization of pairs of graphs whose join graphs are 2-minimally nonouterplanar in terms of forbidden subgraphs.

Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87–97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numb...

Bandelt, H.-J. and H.M. Mulder, Pseudo-median graphs are join spaces, Discrete Mathematics 109 (1992) 13-26. Median graphs are known to share a number of geometrica! properties with Euclidean space, as is testified by the fact that median graphs ale (c!osed) join spaces-the segments of the associated join space being the geodesic intervals of the graph. As is shown in this paper the median join...

Abstract PQ-type adjacency polytopes $$\nabla ^PQ _G$$ ∇ P Q G are lattice arising from finite graphs G . There is a connection between and the engineering problem known as power-flow study,...

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].