The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In the paper we examine the existence of such labelings

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... for several families of plane graphs. On d-antimagic labelings of plane graphs | Martin Bača et al. A labeling of type (1, 1, 0) is a bijection from the set {1, 2, . . . , p + q} to the vertices and edges of a graph G. The weight of a face under a labeling is the sum of labels (if present) carried by that face and the edges and vertices on its boundary. A labeling of a plane graph G is called d-antimagic if for every positive integer s the set of s-sided face weights is W s = {a s , a s + d, a s + 2d, . . . , a s + (r s − 1)d} for some integers a s and d ≥ 0, where r s is the number of s-sided faces. We allow different sets W s for different s. If d = 0 then Ko-Wei Lih in [16] called such labeling magic. Ko-Wei Lih [16] described magic (0-antimagic) labelings of type (1, 1, 0) for the wheels, the friendship graphs and the prisms. The magic labelings of type (1, 1, 1) for the grid graphs and the honeycomb are given in [2] and [3], respectively. The concept of the d-antimagic labeling of the plane graphs was defined in [10], where it was also proved that the prism D n has d-antimagic labelings of type (1, 1, 1) for d ∈ {2, 3, 4, 6} and n ≡ 3 (mod 4). The d-antimagic labelings of type (1, 1, 1) for the hexagonal planar maps, the generalized Petersen graph P (n, 2) and the grids can be found in [5], [7] and [8], respectively. Lin et al. in [17] showed that prism D n , n ≥ 3, admits d-antimagic labelings of type (1, 1, 1) for d ∈ {2, 4, 5, 6}. The d-antimagic labelings of type (1, 1, 1) for D n and for several d ≥ 7 are described in [19] . A d-antimagic labeling is called super if the smallest possible labels appear on the vertices. The super d-antimagic labelings of type (1, 1, 1) for antiprisms and for d ∈ {0, 1, 2, 3, 4, 5, 6} are described in [4] , and for disjoint union of prisms and for d ∈ {0, 1, 2, 3, 4, 5} are given in [1] . The existence of super d-antimagic labelings of type (1, 1, 1) for disconnected plane graphs and for plane graphs containing a special Hamilton path is examined in [6] and [12] , respectively. In this paper we examine the existence of super d-antimagic labelings of type (1, 1, 0) for several families of plane graphs. To label the vertices and edges of plane graphs we will use an edge-antimagic vertex labeling and an edge-antimagic total labeling. Simanjuntak, Bertault and Miller in [18] define an (a, d)-edge-antimagic vertex labeling of a (p, q)-graph G = (V, E) as an injective mapping β : V (G) → {1, 2, . . . , p} such that the set of edge-weights {β(u) + β(v) : uv ∈ E(G)} is {a, a + d, a + 2d, . . . , a + (q − 1)d} for two non-negative integers a and d. A bijection α : V (G)∪E(G) → {1, 2, . . . , p+q} is called an (a, d)edge-antimagic total labeling of G if the edge-weights {α(u) + α(uv) + α(v) : uv ∈ E(G)} form an arithmetic sequence starting at a and having a common difference d, where a > 0 and d ≥ 0 are two fixed integers. An (a, d)-edge-antimagic total labeling is a natural extension of a notion of magic valuation defined by Kotzig and Rosa in [15] . An (a, d)-edge-antimagic total labeling is called super if the smallest possible labels appear on the vertices. A super (a, d)-edge-antimagic total labeling is a natural extension of a notion of super edge-magic labeling defined by Enomoto et al. in [13] . More comprehensive information on magic valuations and (a, d)-edge-antimagic total labelings can be found in [11], [14] and [20], respectively.