Vertex-magic total labelings of even complete graphs

Magic Graphs

“…There are no solutions for k = 15. For k = 16, one obtains (1, 5, 9, 3, 7) (the solution from Theorem 2.19) and also (1,7,3,4,10). Many other possible sets S must be considered when k = 15 or 16, but all can be eliminated using the following observation.…”

“…Notice that two non-isomorphic solutions have the same set of vertex labels. There is one solution for k = 18, (1,8,4,2,5,10), and six for k = 19, namely (1,6,11,3,7,8), (1,7,3,12,5,8), (1,8,7,3,5,12), (1,8,9,4,3,11), (2,7,11,3,4,9), and (3, 4, 5, 6, 11, 7).…”

“…Students see some small graphtheoretic proofs and get some idea of how different areas of graph theory interact (as, for example, when Vizing's Theorem on edge-chromatic number is used). 3. In recent years a number of researchers have found the topic fascinating; unfortunately, they have not all communicated very well with each other, and we hope this volume will obviate unnecessary repetition of intellectual effort and help unify the notation, which is currently diverse and self-contradictory.…”

Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

“…. , n q ) is a super (b, 0)-edge-antimagic total graph, then (5l 2 + (9 -2q )l + (q 2 − r )) ≤ b ≤ (5l 2 + − ( 2 )), where l = ∑ .For d ∈ {0, 1, 2, 3,4,5}, [13] derived the following bounds of lower and upper limits of a on the same subdivided stars class:…”

“…• [12,13] called the star of subdivided T (m, n, k) as a three-path tree and proved that it is a super (b, 0)-EAT if m and n are odd functions with or [12] Verified that T (m, n, k) also admits a super (b, 0)-labeling of edge-antimagic total if m and n are odd functions with or .…”