Plane four-regular graphs with vertex-to-vertex unit triangles

Packing interval graphs with vertex-disjoint triangles

We show that there exists a polynomial algorithm to pack interval graphs with vertex-disjoint triangles.

Constructing vertex decomposable graphs

‎Recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎In this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎Then we use this construction to generalize the result due to Cook and Nagel‎.

Regular vertex diameter critical graphs

A graph is called vertex diameter critical if its diameter increases when any vertex is removed. Regular vertex diameter critical graphs of every valency k ≥ 2 and diameter d ≥ 2 exist, raising the question of identifying the smallest such graphs. We describe an infinite family of k-regular vertex diameter critical graphs of diameter d with at most kd+ (2k − 3) vertices. This improves the previ...

Regular graphs with maximal energy per vertex

The robust vertex centdian location problem with interval vertex weights on general graphs

In this paper, the robust vertex centdian  location  problem with uncertain vertex weights on general graphs is studied. The used criterion to solve the problem is the min-max  regret criterion. This problem  is  investigated  with objective function contains $lambda$  and  a polynomial time algorithm for the problem is presented. It is shown that the vertex centdian problem on general graphs i...