Abstract
Let G(V, E) be a finite connected simple graph with vertex set V(G). A function is a signed dominating function f : V(G)→{−1,1} if for every vertex v ∈ V(G), the sum of closed neighborhood weights of v is greater or equal to 1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate the signed domination numbers of the Cartesian product of two paths Pm and Pn for m = 6, 7 and arbitrary n.
Highlights
Let G be a finite simple connected graph with vertex set V(G)
[6] Hosseini gave a lower and upper bound for the signed domination number for any graph
We studied the signed domination numbers of the Cartesian product of two paths Pm and Pn for m = 6, 7 and arbitrary n
Summary
Let G be a finite simple connected graph with vertex set V(G). The neighborhood of v, denoted N(v), is set {u: uv ∈ E(G)} and the closed neighborhood of v, denoted N[v], is set N(v) ∪ {v}. |Bj| = 4: The j + 1th column includes at most one of the B set vertices, except case (1, j), (3, j), (5, j), (7, j) ∈ B. the j + 1th column includes two of the B set vertices (Figure 16).
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