Deepa Sinha and Pravin Garg

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

Volume 19, 2013, Number 3, Pages 70–77

**Full paper (PDF, 164 Kb)**

## Details

### Authors and affiliations

Deepa Sinha

*Department of Mathematics, South Asian University, Akbar Bhawan
Chanakyapuri, New Delhi–110021, India*

Pravin Garg

*Centre for Mathematical Sciences, Banasthali University
Banasthali–304022, Rajasthan, India*

### Abstract

The canonical marking on a signed graph (or sigraph, in short) S is defined as: for each vertex v ∈ V (S), μ_{σ}(v) = Π_{ej ∈ Ev}, where E_{v} is the set of edges e_{j} incident at v in S. If S is canonically marked, then a cycle Z in S is said to be canonically consistent (C-consistent) if it contains an even number of negative vertices and the given sigraph S is C-consistent if every cycle in it is C-consistent. The total sigraph T(S) of a sigraph S = (V, E, σ) has T(S^{e}) as its underlying graph and for any edge uv of T(S^{e}),

In this paper, we establish a characterization of canonically consistent total sigraphs.

### Keywords

- Sigraph
- Canonical marking
- Consistent sigraph
- Total sigraph

### AMS Classification

- 05C22
- 05C75

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## Cite this paper

Sinha, D., & Garg, P. (2013). A characterization of canonically consistent total signed graphs. *Notes on Number Theory and Discrete Mathematics*, 19(3), 70-77.