Some constructions on total labelling of m triangles
- Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Jalan Sungai Long, Bandar Sungai Long, Cheras 43000 Kajang, Selangor (Malaysia)
Let mK{sub 3} = (V{sub m}, E{sub m}) be a finite disconnected graph consisting of m disjoint triangles K{sub 3}, where V{sub m} is the set of vertices, E{sub m} is the set of edges and both V{sub m} and E{sub m} are of the same size 3m. A total labelling of mK{sub 3} is a function f which maps the elements in V{sub m} and E{sub m} to positive integer values, i.e. f : V{sub m} ∪ E{sub m} → {1, 2, 3,···}. Let c be a positive integer. A triangle is said have a c-Erdősian triangle labelling if it is a total labelling f : V{sub m} ∪ E{sub m} → {c, c + 1, ···, c + 6m − 1} such that f (x) + f (y) = f (xy) for any x, y ∈ V{sub m} and an edge xy ∈ E{sub m} joining them. In order to find all the c-Erdősian triangle labelling, a straightforward is to use the exhaustive search. However, the exhaustive search is only able to find c-Erdősian triangle labelling for m ≤ 5 due to combinatorial explosion. By studying the constant sum of vertex labels, we propose a strong permutation approach, which allows us to generate a certain classes of c-Erdősian triangle labelling up until m = 8.
- OSTI ID:
- 22609038
- Journal Information:
- AIP Conference Proceedings, Vol. 1739, Issue 1; Conference: ICMSS2016: 2. international conference on mathematical sciences and statistics, Kuala Lumpur (Malaysia), 26-28 Jan 2016; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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