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The set of distinct signed degrees of the vertices in a signed graph is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of integers is the signed degree set of some connected signed graph.
Let D be a finite and simple digraph with the vertex set V(D), and let f:V(D) → -1,1 be a two-valued function. If for each v ∈ V(D), where N¯[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V(D)) is called the weight w(f) of f. The minimum of weights w(f), taken over all signed dominating functions f on D, is the signed domination number of D. A set of signed dominating functions on D with the property that for each...
We investigate signed graphs with just 2 or 3 distinct eigenvalues, mostly in the context of vertex-deleted subgraphs, the join of two signed graphs or association schemes.
A signed graph (or sigraph in short) is an ordered pair , where is a graph G = (V,E), called the underlying graph of S and σ:E → +, - is a function from the edge set E of into the set +,-, called the signature of S. The ×-line sigraph of S denoted by is a sigraph defined on the line graph of the graph by assigning to each edge ef of , the product of signs of the adjacent edges e and f in S. In this paper, first we define semi-total line sigraph and semi-total point sigraph of a given...
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