Super antimagic total labeling of graphs
- Authors: Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin
- Date: 2008
- Type: Text , Journal article
- Relation: Utilitas Mathematica Vol. 76, no. (2008), p. 161-171
- Full Text: false
- Reviewed:
- Description: Let G = (V, E) be a simple, finite and undirected graph with v vertices and e edges, A graph labeling is a mapping from elements of a graph to a set of numbers (usually positive integers). If the domain of the mapping is the set of vertices (or edges) then the labeling is called vertex-labeling (or edge-labeling). If the domain of the mapping is the set of vertices and edges then the labeling is called total labeling. The sum of all labels associated with a graph element is called the weight of the element. If the weights of vertices (or the weights of edges) form an arithmetic progression starting at a and with difference d, then the labeling is called (a, d)-vertex-antimagic (or (a, d)-edge-antimagic). Such a labeling is called v-super (or e-super) if the smallest labels appear on the vertices (or edges). In this paper we present new results for v-super vertex-antimagic total and e-super edge-antimagic total labeling.
- Description: C1
Antimagic labelings of grids
- Authors: Baca, Martin , Lin, Yuqing , Miller, Mirka
- Date: 2007
- Type: Text , Journal article
- Relation: Utilitas Mathematica Vol. 72, no. (2007), p. 65-75
- Full Text: false
- Reviewed:
- Description: In this paper we deal with the problem of labeling the vertices, edges and faces of a grid graph by the consecutive integers from 1 to |V| + |E| + |F| in such a way that the label of a face and the labels of the vertices and edges surrounding that face all together add up to a weight of that face. These face weights then form an arithmetic progression with common difference d.
- Description: C1
- Description: 2003004808
Survey of edge antimagic labelings of graphs
- Authors: Miller, Mirka , Baca, Martin , Baskoro, Edy , Ryan, Joe , Simanjuntak, Rinovia , Sugeng, Kiki Ariyanti
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Indonesian Mathematical Society, MIHMI Vol. 12, no. 1 (2006), p. 113-130
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003001600
(a,d)-edge-antimagic total labelings of caterpillars
- Authors: Miller, Mirka , Sugeng, Kiki Ariyanti , Slamin, , Baca, Martin
- Date: 2005
- Type: Text , Journal article
- Relation: Combinatorial Geometry and Graph Theory, LNCS 3330, Lecture Notes in Computer Science, Indonesia-Japan Joint Conference IJCCGGT 2003, Bandung, Indonesia, September 2003, Revised Selected Papers Vol. 3330, no. (2005), p. 169-180
- Full Text: false
- Reviewed:
- Description: For a graph G = (V,E), a bijection g from V (G)∪E(G) into {1, 2, ..., |V (G)|+|E(G)|} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a, d)-edge-antimagic total labeling g is called super (a, d)-edge-antimagic total if g(V (G)) = {1, 2, ..., |V (G)|}. We study super (a, d)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr .
- Description: C1
- Description: 2003001412
Conjectures and open problems on face antimagic evaluations of graphs
- Authors: Miller, Mirka , Baca, Martin , Baskoro, Edy , Cholily, Yus Mochamad , Jendrol, Stanislav , Lin, Yuqing , Ryan, Joe , Simanjuntak, Rinovia , Slamin, , Sugeng, Kiki Ariyanti
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Indonesian Mathematical Society MIHMI Vol. 11, no. 2 (2005), p. 175-192
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003001408
Relationship between adjacency matrices and super (a,d)-edge-antimagic total labeling of graphs
- Authors: Miller, Mirka , Sugeng, Kiki Ariyanti
- Date: 2005
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 71-82
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003001403
Super (a,d)-vertex-antimagic total labelings
- Authors: Miller, Mirka , Sugeng, Kiki Ariyanti , Lin, Yuqing , Baca, Martin
- Date: 2005
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 91-102
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003001401
On d-antimagic labelings of prisms
- Authors: Lin, Yuqing , Slamin, , Baca, Martin , Miller, Mirka
- Date: 2004
- Type: Text , Journal article
- Relation: Ars Combinatoria: A Canadian Journal of Combinatorics Vol. 72, no. (2004), p. 65-76
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003000907