On Modular-$2q$ Graphic Groups Of Topological Coding For Graphic Passwords
Meimei Zhao, Yao Ming, Bing Yao · 2020
Since encrypting networks wholly by graphic groups, we will define a new labelling, called modular- 2q mixed odd-graceful labelling, and build up various graphic groups based on the modular- 2q mixed odd-graceful labelling. We will show: the necessity and sufficiency of subgroup of a graphic group; a ( p, q) -graph G admitting a modular- 2q mixed(negative) odd-graceful labelling can generate a graphic group, and moreover these graphs form an Abelian additive graphic group. A ( p, q) -graph G admits a modular- 2q odd-graceful labelling f generate 2q vertex-modular graphs, each of them generates 2q edge-modular graphs, which form an Abelian additive graphic group, similar results can be obtained for modular- 2q negative odd-graceful graph and modular- 2q mixed odd-graceful graph.