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On Super (a, d)-H-Antimagic Total Covering of Star Related Graphs

100%
Kathiresan K. M., Laurence S. D.
Discussiones Mathematicae Graph Theory
|
2015
|
tom 35
|
nr 4
755-764
EN
Let G = (V (G),E(G)) be a simple graph and H be a subgraph of G. G admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G is a bijection λ: V (G) ∪ E(G) → {1, 2, 3, . . . , |V (G)| + |E(G)|} such that for all subgraphs H′ isomorphic to H, the H′ weights [...] constitute an arithmetic progression a, a+d, a+2d, . . . , a+(n−1)d where a and d are positive integers and n is the number of subgraphs of G isomorphic to H. Additionally, the labeling λ is called a super (a, d)-H-antimagic total labeling if λ(V (G)) = {1, 2, 3, . . . , |V (G)|}. In this paper we study super (a, d)-H-antimagic total labelings of star related graphs Gu[Sn] and caterpillars.
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Characterization Of Super-Radial Graphs

81%
Kathiresan K. M., Marimuthu G., Parameswaran C.
Discussiones Mathematicae Graph Theory
|
2014
|
tom 34
|
nr 4
829-848
EN
In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R*(G) based on G has the vertex set as in G and two vertices u and v are adjacent in R*(G) if the distance between them in G is greater than or equal to d(G) − r(G) + 1 in G. If G is disconnected, then two vertices are adjacent in R*(G) if they belong to different components. A graph G is said to be a super-radial graph if it is a super-radial graph R*(H) of some graph H. The main objective of this paper is to solve the graph equation R*(H) = G for a given graph G.
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