Title of article :
ON SUPER (a, d)-EAT VALUATION OF SUBDIVIDED CATERPILLAR
Author/Authors :
RAHEEM, A Department of Mathematics - National University of Singapore, Singapore , JAVAID, M Department of Mathematics - School of Science - University of Management and Technology, Pakistan , UMAR, M. A Department of Mathematics - Govenment Degree Boys College (B) - Sharqpur Shareef, Pakistan , LAU, G. C Faculty of Computer and Mathematical Sciences - Universiti Teknologi MARA Johor - Segamat, Malaysia
Abstract :
Let G = (V (G), E(G)) be a graph with v = |V (G)| vertices and e = |E(G)|
edges. A bijective function λ : V (G) ∪ E(G) ↔ {1, 2, . . . , v + e} is called an (a, d)-
edge antimagic total (EAT) labeling(valuation) if the weight of all the edges {w(xy) :
xy ∈ E(G)} form an arithmetic sequence starting with first term a and having common
difference d, where w(xy) = λ(x) + λ(y) + λ(xy). And, if λ(V ) = {1, 2, . . . , v} then G
is super (a, d)-edge antimagic total(EAT) graph. In this paper, we determine the super
(a,d)-edge antimagic total (EAT) labeling of the subdivided caterpillar for different values
of the parameter d.
Keywords :
caterpillar , subdivided caterpillar , super(a, d)-EAT graph
Journal title :
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
