# Sign-Compatibility of Some Derived Signed Graphs

### Abstract

A *signed graph* (or *sigraph* in short) is an ordered pair *S* = (*Su*, *σ*), where* Su* is a graph *G* = (*V*, *E*), called the* underlying graph* of *S* and *σ* : *E* → {+1, −1} is a function from the edge set *E* of *Su* into the set {+1, −1}, called the *signature* of *S*. A sigraph *S* is *sign-compatible* if there exists a *marking* *µ* of its vertices such that the end vertices of every negative edge receive ‘−1’ marks in *µ* and no positive edge does so. In this paper, we characterize *S* such that its ×-line sigraphs, semi-total line sigraphs, semi-total point sigraphs and total sigraphs are sign-compatible.

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