[PDF] Top 20 Geometric Number of Planar Graphs

... Each vertex of graph G is represented by a point or small circle in the plane. Every edge is represented by a continuous arc or straight line segment. A certain pairs of vertices of graph are joined by two or more edges, ... See full document

... A vertex coloring is an assignment of colors to each ver- tex of a graph G. A proper vertex coloring assigns colors such that no two adjacent vertices share the same color. Mathematically, it can be described as a ... See full document

... Let G be a connected graph with n vertices and m edges, with vertex set V(G) = {1,2,…,n} and edge set E(G). As usual [20], the distance d(x,y|G) between two vertices x, y  V(G) is defined as the length (= number ... See full document

... the number of edges of G and φ induces a bijection φ ∗ from the edge set of G to {a | 1 ≤ a ≤ 3q − 2 and either a ≡ 1(mod3)} given by φ ∗ (uv) = l φ(u)+φ(v) 2 m and the function φ is called one modulo three mean ... See full document

... [4]. Noga Alon. Restricted colorings of graphs. In Surveys in combinatorics, 1993 (Keele), volume 187 of London Math. Soc. Lecture Note Ser., pages 1{33. Cambridge Univ. Press, Cambridge, 1993. [5]. Noga Alon. ... See full document

... in geometric graphs induced by random point sets has also been stud- ied for graphs related to the Delaunay, including Gabriel graphs [18] and relative neighborhood (RNG) graphs [17, ... See full document

... the number of edges on its boundary; a bounded face is a face with finite length; a plane graph has bounded codegree if there is an upper bound on the length of bounded ... See full document

... Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic ... See full document

... the graphs are simply models of ...fuzzy graphs was given by Kaufman, ...fuzzy graphs during the same ...fuzzy graphs and give some operations on ...fuzzy graphs. The concept of fuzzy ... See full document

... the number of electrical pathways is to great in comparison to the number of electrical components preventing us from placing the circuit on a single circuit ...require graphs that can be decomposed ... See full document

... the number of vertices in a largest clique of G denoted by ω(G), is called the clique number of ...chromatic number of G, denoted by χ(G), is the minimum number of colors which can be assigned ... See full document

... the number of walks and closed walks in a ...the number of closed walks in a graph in terms of the number of vertices, number of edges, maximum degree, degree sequence, and the Zagreb indices ... See full document

... smaller number of edges and still well preserving the cut structure, spectral properties, pairwise distances, transitive closure of G, ...the number of vertices, which is most appealing when only the ... See full document

... Fullerene graphs are the graphical representation of fullerene molecules, an important class of carbon molecules that has became very important in material science and ...fullerene graphs have attracted the ... See full document

... of graphs, namely (f, δ) -embeddability, provides a method to bound the order of the multipartite Ramsey numbers on the ...of graphs, including trees, graphs of bounded degree, and planar ... See full document

... odd number of such paths together forces at least one copy to be traversed with paths that enter and exit through the two upper or lower vertices, and hence must have a subcycle of length at most ... See full document

... line graphs have been introduced and studied by many (see [4, 13, 14], for ...derived graphs was inspired by line ...line graphs can be looked at in a number ... See full document

... the number of edges should be taken into ...different number of ...considered graphs is investigated, then it is observed that the results for the graphs L(W 2n ) and L(f n ), also L(SF n ), ... See full document

... of graphs with interesting structure is high-genus near-planar ...These graphs have a high genus, where the number of crossings would be ω(1), ...constant number of topological handles ... See full document

... The strategy of the proof is the following. We consider three independent simple random walk trajectories, and argue that if each two of them intersect only finitely many times, then they divide our planar graph ... See full document