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Motivated by definition of distance magic labelling, we introduce a new type of irregular labelling whose evaluation is based on the neighbourhood of a vertex. We define a distance irregular labelling on a ...

This paper discusses some characterization and exact values for metric dimension of edge-corona from a connected graph not tree G with an arbitrary nontrivial graph H.

Let all graphs be a connected and simple graph. A set W = fw g of veretx set of G, the kvector ordered r(vjW) = (d(x; w 1 ); d(x; w 2 1 ; w 2 ); : : : ; d(x; w )) of is a representation of v with respect to W, ...

Let G be a connected and simple graph. A split graph is a graph derived by adding new vertex v 0 in every vertex v such that v 0 adjacent to v in graph G. An m-splitting graph is a graph which has m v 0 -vertices, ...

Distance-irregular labeling was introduced by Slamin, and in his paper he determined the distance-irregular labeling for cycles and wheels of length f0; 1; 2; 5g mod 8. In this paper, we complete his results for cycles and ...

Let G = (V (G); E(G)) be a nontrivial connected graph with an edge coloring c : E(G) ! f1; 2; :::; lg; l 2 N, with the condition that the adjacent edges may be colored by the same colors. A path P in G is called rainbow ...

Let G =(V(G),E(G)) be any connected graph of order n = |V(G)| and measure m = |E(G)|. For an order set of vertices S = { s 1 , s 2 , ..., s k } and a vertex v in G, the adjacency representation of v with respect to ...

The concept of face-antimagic labeling of plane graphs was introduced by Mirka Miller in 2003. This survey aims to give an overview of the recent results obtained in this topic.

For a graph G = (V, E), a subset S of V is called a dominating set if every vertex x in V is either in S or adjacent to a vertex in S. The domination number 𝜸(𝑮) is the minimum cardinality of the dominating set of G. ...