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We define and study a class of graphs, called 2-stab interval graphs (2SIG), with boxicity 2 which properly contains the class of interval graphs. A 2SIG is an axes-parallel rectangle intersection graph where the rectangles have unit height (that is, length of the side parallel to Y-axis) and intersects either of the two fixed lines, parallel to the X-axis,… (More)
Signed graphs are studied since the middle of the last century. Recently, the notion of homomorphism of signed graphs has been introduced since this notion captures a number of well known conjectures which can be reformulated using the definitions of signed homomorphism. In this paper, we introduce and study the properties of some target graphs for signed… (More)
The clique number of an undirected graph G is the maximum order of a complete subgraph of G and is a well-known lower bound for the chromatic number of G. Every proper k-coloring of G may be viewed as a homomorphism (an edge-preserving vertex mapping) of G to the complete graph of order k. By considering homomorphisms of oriented graphs (digraphs without… (More)
In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.
An (m, n)-colored mixed graph G is a graph with its arcs having one of the m different colors and edges having one of the n different colors.
An oriented graph is a directed graph without any cycle of length at most 2. To push a vertex of a directed graph is to reverse the orientation of the arcs incident to that vertex. Klostermeyer and MacGillivray defined push graphs which are equivalence class of oriented graphs with respect to vertex pushing operation. They studied the homomorphism of the… (More)
A (m, n)-colored mixed graph is a graph having arcs of m different colors and edges of n different colors. A graph homomorphism of a (m, n)-colored mixed graph G to a (m, n)-colored mixed graph H is a vertex mapping such that if uv is an arc (edge) of color c in G, then f (u)f (v) is also an arc (edge) of color c. The (m, n)-colored mixed chromatic number χ… (More)