Articles written in Proceedings – Mathematical Sciences
Volume 130 All articles Published: 18 November 2020 Article ID 0066 Article
Graham Higman introduced the concept of januarial as a specific map having two equal sized faces under the action of $\langle x, y : x^2 = y^k = (xy)^l = 1\rangle$ on a finite set. In this paper we take up the question posed by Graham Higman that what is the maximum number of circuits in the subgraph of a simple januarial for any value of $k$? We describe conditions under which januarials are connected and larger januarials are obtained. In an effort to look at topological features of the connected januarial, we find out genus of the januarial, genera of the two faces and number of circuits.
Volume 131, 2021
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