Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for these three graphs the bound k ≤ (n − 1)/2 holds. This result implies that only one of a complem...

The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. We describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlike-threshold, split and threshold graphs. In particular, a known necessary condition for a graph to be an edge c...

TD-Delaunay graphs, where TD stands for triangular distance, is a variation of the classical Delaunay triangulations obtained from a specific convex distance function [5]. In [2] the authors noticed that every triangulation is the TD-Delaunay graph of a set of points in R, and conversely every TD-Delaunay graph is planar. It seems natural to study the generalization of this property in higher d...

A Steinhaus matrix is a binary square matrix of size n which is symmetric, with diagonal of zeros, and whose upper-triangular coefficients satisfy ai,j = ai−1,j−1+ai−1,j for all 2 6 i < j 6 n. Steinhaus matrices are determined by their first row. A Steinhaus graph is a simple graph whose adjacency matrix is a Steinhaus matrix. We give a short new proof of a theorem, due to Dymacek, which states...

Graphs are powerful mathematical modeling tools used in various fields of computer science, in particular, in Pattern Recognition. Graph matching is the main operation in Pattern Recognition using graph-based approach. Finding solutions to the problem of graph matching that ensure optimality in terms of accuracy and time complexity is a difficult research challenge and a topical issue. In this ...

Supergrid graphs are derived by computing stitch paths for computerized embroidery machines. In the past, we have studied Hamiltonian-related properties of supergrid and their subclasses graphs. this paper, propose a generalized graph class called extended Extended include grid graphs, diagonal triangular as study problems domination independent on A dominating set is subset vertices it, such t...

For each proper subgraph H of K5, we determine all pairs (k, d) such that every H-minor-free graph is (k, d)-choosable or (k, d)-choosable. The main structural lemma is that the only 3-connected (K5 − e)-minor-free graphs are wheels, the triangular prism, and K3,3; this is used to prove that every (K5 − e)-minor-free graph is 4-choosable and (3, 1)-choosable.