Related papers: 2-semi-equivelar maps on the torus and Klein bottl…
Semi-Equivelar maps are generalizations of maps on the surfaces of Archimedean solids to surfaces other than the $2$-sphere. The well known 11 types of normal tilings of the plane suggest the possible types of semi-equivelar maps on the…
Semi-Equivelar maps are generalizations of Archimedean Solids (as are equivelar maps of the Platonic solids) to the surfaces other than $2-$Sphere. We classify some semi equivelar maps on surface of Euler characteristic -1 and show that…
We present enumerations of a class of maps on Klein bottle which give rise to semi-equivelar maps. Semi-equivelar maps are generalizations of equivelar maps. There are eleven types of semi-equivelar maps on the Klein bottle. These are of…
Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. In earlier work a complete classification of semi-equivelar map of type $(3^5, 4)$ on the surface of Euler characteristic -1 was given. In…
A vertex-transitive map $X$ is a map on a closed surface on which the automorphism group ${\rm Aut}(X)$ acts transitively on the set of vertices. If the face-cycles at all the vertices in a map are of same type then the map is said to be a…
A vertex $v$ in a map $M$ has the face-sequence $(p_1 ^{n_1}. \ldots. p_k^{n_k})$, if there are $n_i$ numbers of $p_i$-gons incident at $v$ in the given cyclic order, for $1 \leq i \leq k$. A map $M$ is called a semi-equivelar map if each…
Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types $\{3^{3},4^{2}\}$, $\{3^{2},4,3,4\}$, $\{6,3,6,3\}$, $\{3^{4},6\}$, $\{4,8^{2}\}$,…
If the face-cycles at all the vertices in a map on a surface are of same type then the map is called semi-equivelar. There are eleven types of Archimedean tilings on the plane. All the Archimedean tilings are semi-equivelar maps. If a map…
If the face\mbox{-}cycles at all the vertices in a map are of same type then the map is called semi\mbox{-}equivelar. In particular, it is called equivelar if the face-cycles contain same type of faces. A map is semiregular (or almost…
A vertex-transitive map $X$ is a map on a surface on which the automorphism group of $X$ acts transitively on the set of vertices of $X$. If the face-cycles at all the vertices in a map are of same type then the map is called a…
If the cyclic sequence of faces for all the vertices in a map are of same type, then the map is said to be a semi-equivelar map. In this article, we classify all the types of semi-equivelar maps on the surface of Euler genus 3, $i.e.$, on…
If every vertex in a map has one out of two face-cycle types, then the map is said to be $2$-semiequivelar. A 2-uniform tiling is an edge-to-edge tiling of regular polygons having $2$ distinct transitivity classes of vertices. Clearly, a…
If the face\mbox{-}cycles at all the vertices in a map are of the same type, then the map is said to be a semi-equivelar map. Automorphism (symmetry) of a map can be thought of as a permutation of the vertices which preserves the…
We enumerate and classify all the semi equivelar maps on the surface of $ \chi=-2 $ with up to 12 vertices. We also determine which of these are vertex-transitive and which are not.
The well-known twenty types of 2-uniform tilings of the plane give rise infinitely many doubly semi-equivelar maps on the torus. In this article, we show that every such doubly semi-equivelar map on the torus contains a Hamiltonian cycle.…
If the face\mbox{-}cycles at all the vertices in a map are of same type then the map is called semi\mbox{-}equivelar. A map is called minimal if the number of vertices is minimal. We know the bounds of number of vertex orbits of…
The second part of the paper is devoted to enumeration of $r$-regular toroidal maps up to all homeomorphisms of the torus (unsensed maps). We describe in detail the periodic orientation reversing homeomorphisms of the torus which turn out…
If the cyclic sequences of {face types} {at} all vertices in a map are the same, then the map is said to be a semi-equivelar map. In particular, a semi-equivelar map is equivelar if the faces are the same type. Homological quantum codes…
A Lorentz surface in the four-dimensional pseudo-Euclidean space with neutral metric is called quasi-minimal if its mean curvature vector is lightlike at each point. In the present paper we obtain the complete classification of…
Applying the Hric-J\"ager blow up technique, we give an affirmative answer to the question about the existence of non-invertible minimal circle-fibered self-maps of the Klein bottle. In addition, we present a simpler construction of a…