On the Number of Edges in a Minimum C6-Saturated Graph

Eternal m- Security Subdivision Numbers in Graphs

Let  be a simple graph with vertex set  and edges set . A set  is a dominating set if every vertex in  is adjacent to at least one vertex  in . An eternal 1-secure set of a graph G is defined as a dominating set  such that for any positive integer k and any sequence  of vertices, there exists a sequence of guards   with  and either  or  and  is a dominating set. If we take a guard on every ver...

On the revised edge-Szeged index of graphs

The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...

Total domination in $K_r$-covered graphs

The inflation $G_{I}$ of a graph $G$ with $n(G)$ vertices and $m(G)$ edges is obtained from $G$ by replacing every vertex of degree $d$ of $G$ by a clique, which is isomorph to the complete graph $K_{d}$, and each edge $(x_{i},x_{j})$ of $G$ is replaced by an edge $(u,v)$ in such a way that $uin X_{i}$, $vin X_{j}$, and two different edges of $G$ are replaced by non-adjacent edges of $G_{I}$. T...

The Maximum Number of Edges in a Strongly Multiplicative Graph

A note on minimum K2, 3-saturated graphs

A graph G is said to be K2,3-saturated if G contains no copy of K2,3 as a subgraph, but for any edge e in the complement of G the graph G + e does contain a copy of K2,3. The minimum number of edges of a K2,2-saturated graph of given order n was precisely determined by Ollmann [6]. Here, we determine the asymptotic behavior for the minimum number of edges in a K2,3-saturated graph.