Binary operation graphs
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CitationAl-Harere, M. N., Omran, A. A. A. (2019). Binary operation graphs. International Conference of Mathematical Sciences. s. 030008(1)-030008(3).
A graph labeling is an assignment of integers to the vertices, edges, or to both, and it is subject to certain conditions. In this paper, a new concept of graph labeling called binary operation labeling is introduced. Let G = (V, E) be a (n, m)-graph and let f : V(G) → 1, 2, ..., n be a bijection. We define f ∗ on E(G) by f ∗ (uv) = (f(u) + f(v))/2 if both f(u) and f(v) are odd or both are even and f ∗ (uv) = (f(u)f(v))/2 if u is odd and v is even or vice versa for each uv ∈ E(G). If f ∗ is injective on E(G), then f is called a binary operation labeling. The graph G is said to be a binary operation graph if G admits a binary operation labeling. Some results for this new type of labeling are contributed.
SourceInternational Conference of Mathematical Sciences
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