### authors

- CARBALLOSA TORRES, WALTER
- De la Cruz, A.
- RODRIGUEZ GARCIA, JOSE MANUEL

- Overview

- March 2017

- 1017-060X

- 1735-8515

- In this paper we characterize the hyperbolic product graphs for the Cartesian sum G1⊕G2: G1⊕G2 is always hyperbolic, unless either G1 or G2 is the trivial graph (the graph with a single vertex); if G1 or G2 is the trivial graph, then G1⊕G2 is hyperbolic if and only if G2 or G1 is hyperbolic, respectively. Besides, we characterize the Cartesian sums with hyperbolicity constant delta(G1⊕G2)=t for every value of t. Furthermore, we obtain the sharp inequalities 1≤delta(G1⊕G2)≤3/2 for every non-trivial graphs G1,G2. Also, we obtain simple formulas for the hyperbolicity constant of the Cartesian sum of many graphs. Finally, we prove the inequalities 3/2≤delta(G1⊕G2)≤2 for the complement graph of G1⊕G2 for every G1,G2 with min{diamV(G1),diamV(G2)}≥3.

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Universidad Carlos III de Madrid
(data updated on January 28, 2019)
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