- Title
- Construction of new larger (a, d)-edge antimagic vertex graphs by using adjacency matrices
- Creator
- Rahmawati, S.; Sugeng, K. A.; Silaban, D. R.; Miller, M.; Bača, M.
- Relation
- Australasian Journal of Combinatorics Vol. 56, p. 257-272
- Publisher
- Centre for Discrete Mathematics and Computing, University of Queensland
- Resource Type
- journal article
- Date
- 2013
- Description
- Let G = G(V,E) be a finite simple undirected graph with vertex set V and edge set E, where ∣E∣ and ∣V∣ are the number of edges and vertices on G. An (a, d)-edge antimagic vertex ((a, d)-EAV) labeling is a one-to-one mapping f from V (G) onto {1, 2...,∣V∣} with the property that for every edge xy ∈ E, the edge-weight set is equal to {f(x) + f(y): x, y ∈ V } = {a, a+d, a+2d,..., a+(∣E∣-1)d}, for some integers a > 0, d ≥ 0. An (a, d)-edge antimagic total ((a, d)-EAT) labeling is a one-toone mapping f from V ∪ E onto {1, 2,...,∣V∣ + ∣E∣} with the property that for every edge xy ∈ E, the edge-weight set is equal to {f(x)+f(y)+ f(xy): x, y ∈ V, xy ∈ E} = {a, a+d, a+2d,..., a+(∣E∣-1)d}, where a > 0, d ≥ 0 are two fixed integers. Such a labeling is called a super (a, d)- edge antimagic total ((a, d)-SEAT) labeling if f(V) = {1, 2,...,∣V∣}. A graph that has an (a, d)-EAV ((a, d)-EAT or (a, d)-SEAT) labeling is called an (a, d)-EAV ((a, d)-EAT or (a, d)-SEAT) graph. For an (a, d)- EAV (or (a, d)-SEAT) graph G, an adjacency matrix of G is ∣V∣ × ∣V∣ matrix AG = [aij] such that the entry aij is 1 if there is an edge from vertex with index i to vertex with index j, and entry aij is 0 otherwise. This paper shows the construction of new larger (a, d)-EAV graph from an existing (a, d)-EAV graph using the adjacency matrix, for d = 1, 2. The results will be extended for (a, d)-SEAT graphs with d = 0, 1, 2, 3.
- Subject
- antimagic vertex graphs; adjacency matrices
- Identifier
- http://hdl.handle.net/1959.13/1311555
- Identifier
- uon:22239
- Identifier
- ISSN:1034-4942
- Language
- eng
- Full Text
- Reviewed
- Hits: 3477
- Visitors: 3660
- Downloads: 213
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT02 | Publisher version (open access) | 188 KB | Adobe Acrobat PDF | View Details Download |