P. Siva Kota Reddy and M. S. Subramanya

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 15, 2009, Number 4, Pages 1—6

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## Details

### Authors and affiliations

P. Siva Kota Reddy

*Department of Studies in Mathematics
University of Mysore, Manasagangotri
Mysore 570 006, India
*

M. S. Subramanya

*Department of Studies in Mathematics
University of Mysore, Manasagangotri
Mysore 570 006, India
*

### Abstract

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* P_{k}(G) of a graph G is obtained by representing the paths P_{k} in G by vertices whenever the corresponding paths P_{k} in G form a path P_{k+1} or a cycle C_{k}. 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, P_{k}(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 P_{3}(S) (P_{4}(S)).

### Keywords

- Signed graphs
- Balance
- Switching
- Line signed graphs
- Path signed graphs
- Negation

### AMS Classification

- 05C22

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## Cite this paper

APASiva Kota Reddy, P. & Subramanya, M. S. (2009). Note on path signed graphs. Notes on Number Theory and Discrete Mathematics, 15(4), 1-6.

ChicagoSiva Kota Reddy, P, and MS Subramanya. “Note on Path Signed Graphs.” Notes on Number Theory and Discrete Mathematics 15, no. 4 (2009): 1-6.

MLASiva Kota Reddy, P, and MS Subramanya. “Note on Path Signed Graphs.” Notes on Number Theory and Discrete Mathematics 15.4 (2009): 1-6. Print.