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${session.getAttribute("locale")}5Construction of new larger (a, d)-edge antimagic vertex graphs by using adjacency matrices
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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 A_{G} = [a_{ij}] such that the entry a_{ij} is 1 if there is an edge from vertex with index i to vertex with index j, and entry a_{ij} 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.]]>Wed 11 Apr 2018 13:24:44 AEST]]>On distance magic labeling of graphs
https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:8133
Sat 24 Mar 2018 08:40:03 AEDT]]>Clique vertex magic cover of a graph
https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:17756
ί, ί , i = 1, . . . , r of G is isomorphic to H and f(H_{ί})=f(H)=Σ v∈V(H_{ί}) f(v)+Σ e∈V(H_{ί}) f(e)=m(f). In this paper we define a subgraph-vertex magic cover of a graph and give some construction of some families of graphs that admit this property. We show the construction of some C_{n} - vertex magic covered and clique magic covered graphs.]]>Sat 24 Mar 2018 07:57:21 AEDT]]>