A complete classification of 5-regular circulant graphs that allow cyclic orthogonal double covers

Graph theory and its applications attract several researchers from different areas of research. It is used to model wide range of systems, for example in biological system and in studying chaotic systems. Decomposition of complex graphs into simple small graphs is very helpful to study that complex systems. A complete classification is given for circulant graphs of degree 5 that allow an Orthogonal Double Cover by some graphs. Whenever such a cover exists, an orthogonal labelling for the corresponding covering graph is presented. Our work here completes all previous incomplete work about this point.