Independence numbers of some double vertex graphs and pair graphs

Abstract

The combinatorial properties of double vertex graphs has been widely studied since the 90's. However only very few results are know about the independence number of such graphs. In this paper we obtain the independence numbers of the double vertex graphs of fan graphs and wheel graphs. Also we obtain the independence numbers of the pair graphs, that is a generalization of the double vertex graphs, of some families of graphs.

Figures (3)

• Figure 1: Double vertex graph of $F_{4, 1}$. In this case $B=\{\{1, 5\}, \{2, 5\}, \{3, 5\}, \{4, 5\}\}, T_m=V(A_{4, 1}^{(2)})-B$ and $R_2=\{\{1,2\}, \{2, 3\},\{2, 4\}\}$.
• Figure 2: a) Graph $T_8-R_2$, b) graph $T_6-R_1$, c) graph $T_6-(R_2\cup R_5)$.
• Figure 3: Graph $T_{10} -R_2 \cup R_5$

Theorems & Definitions (41)

• Theorem 1.1
• Theorem 1.2
• Theorem 1.3
• Theorem 1.4
• Theorem 1.5
• Theorem 1.6
• Lemma 2.1
• Proposition 2.2
• Proposition 2.3
• Proposition 2.4