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Data in the social sciences can often modeled using signed graphs, graphs where every edge has a sign + or −, or marked graphs, graphs where every vertex has a sign + or −. The path graph Pk(G) of a graph G is obtained by representing the paths Pk in G by vertices whenever the corresponding paths Pk in G form a path Pk+1 or a cycle Ck. In this note, we introduce a natural extension of the notion of path graphs to the realm of signed graphs. It is shown that for any signed graph S, Pk(S) is balanced. The concept of a line signed graph is generalized to that of a path signed graphs. Further, in this note we discuss the structural characterization of path signed graphs. Also, we characterize signed graphs which are switching equivalent to their path signed graphs P3(S) (P4(S)).
- Signed graphs
- Line signed graphs
- Path signed graphs
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Cite this paper
Siva Kota Reddy, P., & Subramanya, M. S. (2009). Note on path signed graphs. Notes on Number Theory and Discrete Mathematics, 15(4), 1-6.