The matching extendability of 7-connected maximal 1-plane graphs

The maximal total irregularity of some connected graphs

The total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈V(G). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.

Acute triangles in 4-connected maximal plane graphs

In this paper, we show that every 4-connected maximal plane graph with m finite faces other than the octahedron can be drawn in the plane so that at least (m+3)/2 faces are acute triangles. Moreover, this bound is sharp. © 2005 Published by Elsevier B.V.

the maximal total irregularity of some connected graphs

the total irregularity of a graph g is defined as 〖irr〗_t (g)=1/2 ∑_(u,v∈v(g))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈v(g). in this paper by using the gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.

Maximal Common Connected Sets of Interval Graphs

Given a pair of graph G1 = (V,E1), G2 = (V,E2) on the same vertex set, a set S ⊆ V is a maximal common connected set of G1 and G2 if the subgraphs of G1 and G2 induced by S are both connected and S is maximal the inclusion order. The maximal Common Connected sets Problem (CCP for short) consists in identifying the partition of V into maximal common connected sets of G1 and G2. This problem has ...

Optimal Orthogonal Drawings of Connected Plane Graphs