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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...
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...
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