TY - JOUR
T1 - Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
TT -
JF - IJMSI
JO - IJMSI
VL - 13
IS - 2
UR - http://ijmsi.ir/article-1-823-en.html
Y1 - 2018
SP - 1
EP - 13
KW - Complete bipartite graphs
KW - Supermagic graphs
KW - Degree-magic graphs
KW - Balanced degree-magic graphs
N2 - A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+|E(G)|)deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper we find the necessary and sufficient conditions for the existence of balanced degree-magic labelings of graphs obtained by taking the join, composition, Cartesian product, tensor product and strong product of complete bipartite graphs.
M3
ER -