Number of Cycles of Length Four in Sum Graphs and Integral Sum Graphs
نویسنده
چکیده
A sum graph is a graph for which there is a labeling of its vertices with positive integers so that two vertices are adjacent if and only if the sum of their labels is the label of another vertex. Integral sum graphs are defined similarly, except that the labels may be any integers. These concepts were first introduced by Harary, who provided examples of such graphs of all orders. The family of integral sum graphs was extended to by Vilfred who calculated number of triangles in , , and , kN andm,n . In this paper, we calculate number of cycles of length four, at first, in graphs and and then using these we obtain that of and , kN andm,n . Also, we prove that for nN, and with-out vertex labels where is the vertex with integral sum labeling j in and anti-integral sum labeling j in , m = n+2 or m = n+4 and 1 ≤ j ≤ m and obtain a few properties of natural numbers. AMS Subject Classification: 05C75, 05C78.
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