We generalize the notion of Jacobson graphs into $n$-array columns called $n$-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an $n$-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.

A graph is 1-planar, if it admits a 1-planar embedding, where each edge has at most one crossing. Unfortunately, testing 1-planarity of a graph is known as NP-complete. This paper considers the problem of testing 2-planarity of a graph, in particular,testing full outer-2planarity of a graph. A graph is fully-outer-2-planar, if it admits a fully-outer-2-planar embedding such that every vertex is...

We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with nice convex drawings: outer k-planar graphs, where each edge is crossed by at most k other edges; and, outer k-quasi-planar graphs where no k edges can mutually cross. We show that the outer k-planar graphs are (b √ 4k + 1...

Any simple planar graph can be triangulated, i.e., we can add edges to it, without adding multi-edges, such that the result is planar and all faces are triangles. In this paper, we study the problem of triangulating a planar graph without increasing the pathwidth by much. We show that if a planar graph has pathwidth k, then we can triangulate it so that the resulting graph has pathwidth O(k) (w...

A graph G is outer projective planar if it can be embedded in the projective plane so that every vertex appears on the boundary of a single face We exhibit obstruction sets for outer projective planar graphs with respect to the subdivision minor and Y orderings Equivalently we nd the minimal non outer projective planar graphs under these orderings

A graph is outer 1-planar if it admits a drawing where each vertex is on the outer face and each edge is crossed by at most another edge. Outer 1-planar graphs are a superclass of the outerplanar graphs and a subclass of the planar partial 3-trees. We show that an outer 1-planar graph G of bounded degree ∆ admits an outer 1-planar straight-line drawing that uses O(∆) different slopes, which gen...

this paper is dedicated to propose an algorithm in order to generate the certain isomers of some well-known fullerene bases. furthermore, we enlist the bipartite edge frustration correlated with some of symmetrically distinct innite families of fullerenes generated by the oered process.

A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. In this paper, we completely determine the edge chromatic number of outer 1-planar graphs.

The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs. It is mentioned that the framework can be applied to obtain an O(2...