A lexicographic product for signed graphs.
A lexicographic product for signed graphs.
Summary: A signed graph is a pair \(\Gamma=(G,\sigma)\), where \(G=(V(G),E(G))\) is a graph and \(\sigma:E(G)\rightarrow\{+1,-1\}\) is the sign function on the edges of \(G\). The notion of composition (also known as lexicographic product) of two signed graphs \(\Gamma\) and \(\Lambda=(H,\tau)\) already exists in literature, yet it fails to map balanced graphs onto balanced graphs. We improve the existing definition showing that our `new' signature on the lexicographic product of \(G\) and \(H\) behaves well with respect to switching equivalence. Signed regularities and some spectral properties are also discussed.
Signed graphs, Lexicographic product, spectral properties, Graph operations (line graphs, products, etc.), Signed graphs, Lexicographic product, Signed and weighted graphs, signed regularities
Signed graphs, Lexicographic product, spectral properties, Graph operations (line graphs, products, etc.), Signed graphs, Lexicographic product, Signed and weighted graphs, signed regularities
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