Hany Ibrahim

activity

20182022

collaborators

5 papers

math.CO2022

Edge Contraction and Line Graphs

Hany Ibrahim, Peter Tittmann

Given a family of graphs $H$ , a graph $G$ is $H$ -free if any subset of $V (G)$ does not induce a subgraph of $G$ that is isomorphic to any graph in $H$ …

math.CO2022

Edge Contraction and Forbidden Induced Graphs

Hany Ibrahim, Peter Tittmann

A graph $G$ is $H$ -free if any subset of $V (G)$ does not induce a subgraph of $G$ that is isomorphic to $H$ . Given a graph $H$ , we present sufficient and necessary conditions for a…

math.CO2021

Characterizations for split graphs and unbalanced split graphs

Hany Ibrahim

We introduce a characterization for split graphs by using edge contraction. Then, we use it to prove that any ( $2 K_{2}$ , claw)-free graph with $α (G) \geq 3$ is a split graph. Also,…

math.CO2019

Note on clique polynomials and independent set polynomial of graphs

Hany Ibrahim

In 1994, Cornelis Hoede and Xueliang Li introduced the clique polynomial of a graph. Also, a theorem for the edge subgraph expansion for clique polynomials. In this note we present…

math.CO2018

Defensive alliance polynomial

Hany Ibrahim

We introduce a new bivariate polynomial which we call the defensive alliance polynomial and denote it by da(G; x, y). It is a generalization of the alliance polynomial [Carballosa…