Authors: G.C. Lau, H.-K. Ng, W.C. Shiu Title: On local antimagic chromatic number of cycle-related join graphs Source: Discussiones Mathematicae Graph Theory Received 21.05.2018, Revised 27.08.2018, Accepted 27.08.2018, doi: 10.7151/dmgt.2177 | |
Abstract: An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it is a bijection f:E →{1,... ,|E|} such that for any pair of adjacent vertices x and y, f^{+}(x)\not= f^{+}(y), where the induced vertex label f^{+}(x)= ∑ f(e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by χ_{la}(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, several sufficient conditions for χ_{la}(H)\le χ_{la}(G) are obtained, where H is obtained from G with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle-related join graphs. | |
Keywords: local antimagic labeling, local antimagic chromatic number, cycle, join graphs | |
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