5 research outputs found

### Cyclic edge extensions-self centered graphs

The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. The maximum
and the minimum eccentricity among the vertices of a graph G are known as the diameter and the radius
of G respectively. If they are equal then the graph is said to be a self - centered graph. Edge addition
/extension to a graph either retains or changes the parameter of a graph, under consideration. In this
paper mainly, we consider edge extension for cycles, with respect to the self-centeredness(of cycles),that
is, after an edge set is added to a self centered graph the resultant graph is also a self-centered graph.
Also, we have other structural results for graphs with edge -extensions

### Edge Jump Distance Graphs

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˘Ă˘â€šÂ¬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 \ â€š E(G) and uw does not belong to â€š 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
 

### On Some Edge Rotation Distance Graphs

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 byâ€ť rotatingâ€ť
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

### Edge Jump Distance Graphs

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 jumps