In thiSpecificallye focus on the MWKverticeslem for areimplacedt class on network graplane
Let H be the 5-vertex graph obtained by attaching a path on two vertices to a vertex of a triangle.
Given a graph G="(V,E) on n vertices, a pair (X,Y), with X,Y⊆V, X∩Y="∅, is a non-induced biclique if {x,y}∈E for any x∈X and y∈Y.
Then a G-decomposition of Kv, a complete graph on v vertices, is a pair Σ="(X,B), where X is the vertex set of Kv and B is a partition of the edge set of Kv into graphs all isomorphic to G. The elements of B are called blocks and Σ is said to be a G-design of order v.
A conference graph on 2m+3 vertices yields a regular Hadamard matrix of order 4(m+1)2.
For a given graph Γ, a Γ-design on v vertices is simply a Γ-decomposition of the complete graph Kv.
D efinition 1 A rooted tree T on n vertices is an n-clonal tree for a mutation set [ n ] = { 1, …, n } provided each edge is labeled with exactly one mutation from [ n ] and no mutation appears more than once in T. Let T n be the set of all n-clonal trees.
A rooted tree T on n vertices is an n-clonal tree for a mutation set [ n ] = { 1, …, n } provided each edge is labeled with exactly one mutation from [ n ] and no mutation appears more than once in T. Let T n be the set of all n-clonal trees.
It is proved that the join of an empty graph on v−1 vertices and a cycle graph on v+1 vertices is the unique trace-minimal graph in this class.
Let G be a graph on n vertices, which is an edge-disjoint union of ms-factors, that is, s regular spanning subgraphs.
