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*in

_{k}*G*by vertices whenever the corresponding paths

*P*in

_{k}*G*form a path

*P*

_{k+1}or a cycle

*C*. 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

_{k}*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

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