Vertex Cover Gets Faster and Harder on Low Degree Graphs

Some Results on Forgotten Topological Coindex

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

Bounding cochordal cover number of graphs via vertex stretching

It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...

Faster computation of maximum independent set and parameterized vertex cover for graphs with maximum degree 3

Maximum Independent Set in Graphs of Average Degree at Most Three in O(1.08537n){\mathcal O}(1.08537^n)

We show that Maximum Independent Set on connected graphs of average degree at most three can be solved in O(1.08537) time and linear space. This improves previous results on graphs of maximum degree three, as our connectivity requirement only functions to ensure that each connected component has average degree at most three. We link this result to exact algorithms of Maximum Independent Set on ...

On reverse degree distance of unicyclic graphs

The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...