MATCHING AND EDGE COVERING NUMBER ON LEXICOGRAPHICAL PRODUCT OF COMPLETE GRAPHS

META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS

The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...

Detour Monophonic Graphoidal Covering Number of Corona Product Graph of Some Standard Graphs with the Wheel

A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path  $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A  detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex  of at most on...

Product of normal edge-transitive Cayley graphs

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

Covering Arrays on Product Graphs

Two vectors x, y in Zg are qualitatively independent if for all pairs (a, b) ∈ Zg×Zg, there exists i ∈ {1, 2, . . . , n} such that (xi, yi) = (a, b). A covering array on a graph G, denoted by CA(n,G, g), is a |V (G)|×n array on Zg with the property that any two rows which correspond to adjacent vertices in G are qualitatively independent. The number of columns in such array is called its size. ...

Edge covering of acyclic graphs