Star-ladder graphs were introduced by Gross in his development of a quadratic-time algorithm for the genus distribution of a cubic outerplanar graph. This paper derives a formula for the genus distribution of star-ladder graphs, using Mohar’s overlap matrix and Chebyshev polynomials. Newly developed methods have led to a number of recent papers that derive genus distributions and total embeddin...

Abstract. A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, an algorithm is determined for skew edge coloring of circular ladder graphs. Alsothe skew chromatic index of circular la...

We consider a specific random graph which serves as disordered medium for particle performing biased walk. Take two-sided infinite horizontal ladder and pick spanning tree with certain edge weight $c$ the (vertical) rungs. Now take walk on that bias $\beta>1$ to right. In contrast other graphs considered in literature (random percolation clusters, Galton-Watson trees) this one allows an explici...

Abstrak. Automorfisma dari suatu graf G merupakan isomorfisma ke dirinya sendiri, yaitu fungsi yang memetakan sendiri. dapat dicari dengan menentukan semua kemungkinan satu-satu, onto serta himpunan titik pada tersebut. Artikel ini difokuskan penentuan banyaknya tangga dan lingkaran automorfisma grup dibentuk oleh kedua Jenis penelitian dasar atau murni metode digunakan adalah studi literatur. ...

A vertex-coloured graph G is said to be rainbow vertex-connected, if every two vertices of are connected by a path whose internal have distinct colours. The vertex-connection number G, denoted rvc(G), the smallest colours that needed make vertex-connected. This study focuses on deriving formulas for vertex connectivity simple ladder and roach graph.

Node embeddings are increasingly used in various analysis tasks of networks due to their excellent dimensional compression and feature representation capabilities. However, most researchers’ priorities have always been link prediction, which leads signed network clustering being under-explored. Therefore, we propose an asymmetric ladder-shaped architecture called RGCLN based on multi-relational...

Let β(G) and Γ(G) be the independence number and the upper domination number of a graphG, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. The class of Γ-perfect graphs generalizes such well-known classes of graphs as strongly perfect graphs, absorbantly perfect graphs, and circular arc graphs. In this article, we present a characterization of Γ-per...

where ai is the number of embeddings, for i = 0, 1, . . ., into the orientable surface Si, and bj is the number of embeddings, for j = 1, 2, . . ., into the non-orientable surface Nj . The sequence {ai(G)|i ≥ 0} ⋃ {bj(G)|j ≥ 1} is called the total embedding distribution of the graph G; it is known for relatively few classes of graphs, compared to the genus distribution {ai(G)|i ≥ 0}. The circul...

We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n + 1 rungs. Such an assignment yields an index one current graph with current group Z12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our charact...