133,274 research outputs found

    New Results on Edge Rotation Distance Graphs

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    The concept of edge rotations and distance between graphs was introduced by Gary Chartrand et al. [3]. A graph G can be transformed into a graph H by an edge rotation if G contains distinct vertices u,v and w such that uv 2 E(G), uw =2 E(G) and H =G􀀀uv +uw. In this case, G is transformed into H by “rotating†the edge uv of G into uw. Let S = G1, G2,...,Gk be a set of graphs all of the same order and the same size. Then the rotation distance graph D(S) of S has S as its vertex set and vertices (graphs) Gi and Gj are adjacent if dr(Gi,Gj ) =1, where dr(Gi, Gj ) is the rotation distance between Gi and Gj .A graph G is a edge rotation distance graph(ERDG) (or r - distancegraph) if G =D(S) for some set S of graphs. In [8]Huilgol et al. have showed that the Generalized Petersen Graph Gp(n; 1), the generalized star Km(1; n) is a ERDG. In this paper we consider rotations on some particular graphs Triangular Snake, Double Triangular Snake, Alternating Double Triangular Snake, Quadrilateral Snake, Double Quadrilateral Snake, Alternating Double Quadrilateral snake followed by some generalresults

    Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition

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    A geometric graph is angle-monotone if every pair of vertices has a path between them that---after some rotation---is xx- and yy-monotone. Angle-monotone graphs are 2\sqrt 2-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize angle-monotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized angle-monotone---specifically, we prove that the half-θ6\theta_6-graph is generalized angle-monotone. We give a local routing algorithm for Gabriel triangulations that finds a path from any vertex ss to any vertex tt whose length is within 1+21 + \sqrt 2 times the Euclidean distance from ss to tt. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

    On Some Edge Rotation Distance Graphs

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    The concept of edge rotations and distance between graphs was introduced by Gary Chartrand et.al [1].A graph G can be transformed into a graph H by an edge rotation if G contains distinct vertices u, v and w such uvE(G) and uwE(G) and H G uv uw . In this case, G is transformed into H by” rotating” the edge uv of G into uw. In this paper we consider rotations on generalized Petersen graphs and minimum selfcenteredgraphs. We have also developed algorithms to generate distance degree injective (DDI) graphs and almost distance degree injective (ADDI) graphs from cycles using the concept of rotations followed by some general results

    Distances between graphs under edge operations

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    AbstractWe investigate three metrics on the isomorphism classes of graphs derived from elementary edge operations: the edge move, rotation and slide distances. We derive relations between the metrics, and bounds on the distance between arbitrary graphs and between arbitrary trees. We also consider the sensitivity of the metrics to various graph operations

    Distances in and between graphs.

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    Thesis (M.Sc.)-University of Natal, 1991.Aspects of the fundamental concept of distance are investigated in this dissertation. Two major topics are discussed; the first considers metrics which give a measure of the extent to which two given graphs are removed from being isomorphic, while the second deals with Steiner distance in graphs which is a generalization of the standard definition of distance in graphs. Chapter 1 is an introduction to the chapters that follow. In Chapter 2, the edge slide and edge rotation distance metrics are defined. The edge slide distance gives a measure of distance between connected graphs of the same order and size, while the edge rotation distance gives a measure of distance between graphs of the same order and size. The edge slide and edge rotation distance graphs for a set S of graphs are defined and investigated. Chapter 3 deals with metrics which yield distances between graphs or certain classes of graphs which utilise the concept of greatest common subgraphs. Then follows a discussion on the effects of certain graph operations on some of the metrics discussed in Chapters 2 and 3. This chapter also considers bounds and relations between the metrics defined in Chapters 2 and 3 as well as a partial ordering of these metrics. Chapter 4 deals with Steiner distance in a graph. The Steiner distance in trees is studied separately from the Steiner distance in graphs in general. The concepts of eccentricity, radius, diameter, centre and periphery are generalised under Steiner distance. This final chapter closes with an algorithm which solves the Steiner problem and a Heuristic which approximates the solution to the Steiner problem

    Edge Jump Distance Graphs

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    The concept of edge jump between graphs and distance between graphs was introduced by Gary Chartrand et al. in [5]. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u, v, w, and x such that uv belongs to  E(G), wx does not belong to E(G) and H isomorphic to G ¢â‚¬uv + wx. The concept of edge rotations and distance between graphs was first introduced by Chartrand et.al [4]. A graph H is said to be obtained from a graph G by a single edge rotation if G contains three distinct vertices u, v, and w such that uv belongs to \ ‚ E(G) and uw does not belong to ‚ E(G). If a graph H is obtained from a graph G by a sequence of edge jumps, then G is said to be j-transformed into H. In this paper we consider edge jumps on generalized Petersen graphs Gp(n,1) and cycles. We have also developed an algorithm that gives self-centered graphs and almost self-centered graphs through edge jumps followed by some general results on edge jum &nbsp

    Causal Dynamics of Discrete Surfaces

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    We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.Comment: In Proceedings DCM 2013, arXiv:1403.768
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