Abstract
The crossing number cr(H) of a graph H is the minimum number of edge crossings over all drawings of H in the plane. Let H∗ be the connected graph of order five isomorphic to K5 ∖ e obtained by removing one edge from the complete graph K5. The main aim of the paper is to give the crossing numbers of the join products H∗ + Pn and H∗ + Cn, where Pn and Cn are the path and the cycle on n vertices, respectively. The proofs are done with the help of a suitable classification of a large number of drawings of the graph H∗ in view of the existence of a separating cycle of two possible types.
Communicated by Peter Horák
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© 2024 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- On monoids of endomorphisms of a cycle graph
- The influence of separating cycles in drawings of K5 ∖ e in the join product with paths and cycles
- Completely hereditarily atomic OMLS
- New notes on the equation d(n) = d(φ(n)) and the inequality d(n) > d(φ(n))
- On the monogenity and Galois group of certain classes of polynomials
- Other fundamental systems of solutions of the differential equation (D2 – 2αD + α2 + β2)ny = 0, β ≠ 0
- Characterization of continuous additive set-valued maps “modulo K” on finite dimensional linear spaces
- Hermite–Hadamard inequalities for Riemann–Liouville fractional integrals
- Global Mild Solutions For Hilfer Fractional Neutral Evolution Equation
- The discrete fractional Karamata theorem and its applications
- Complex Generalized Stancu-Schurer Operators
- New oscillatory criteria for third-order differential equations with mixed argument
- Cauchy problem for a loaded hyperbolic equation with the Bessel operator
- Liouville type theorem for a system of elliptic inequalities on weighted graphs without (p0)-condition
- On the rate of convergence for the q-Durrmeyer polynomials in complex domains
- Some fixed point theorems in generalized parametric metric spaces and applications to ordinary differential equations
- On the relation of Kannan contraction and Banach contraction
- Extropy and statistical features of dual generalized order statistics’ concomitants arising from the Sarmanov family
- Residual Inaccuracy Extropy and its properties
- Archimedean ℓ-groups with strong unit: cozero-sets and coincidence of types of ideals
Articles in the same Issue
- On monoids of endomorphisms of a cycle graph
- The influence of separating cycles in drawings of K5 ∖ e in the join product with paths and cycles
- Completely hereditarily atomic OMLS
- New notes on the equation d(n) = d(φ(n)) and the inequality d(n) > d(φ(n))
- On the monogenity and Galois group of certain classes of polynomials
- Other fundamental systems of solutions of the differential equation (D2 – 2αD + α2 + β2)ny = 0, β ≠ 0
- Characterization of continuous additive set-valued maps “modulo K” on finite dimensional linear spaces
- Hermite–Hadamard inequalities for Riemann–Liouville fractional integrals
- Global Mild Solutions For Hilfer Fractional Neutral Evolution Equation
- The discrete fractional Karamata theorem and its applications
- Complex Generalized Stancu-Schurer Operators
- New oscillatory criteria for third-order differential equations with mixed argument
- Cauchy problem for a loaded hyperbolic equation with the Bessel operator
- Liouville type theorem for a system of elliptic inequalities on weighted graphs without (p0)-condition
- On the rate of convergence for the q-Durrmeyer polynomials in complex domains
- Some fixed point theorems in generalized parametric metric spaces and applications to ordinary differential equations
- On the relation of Kannan contraction and Banach contraction
- Extropy and statistical features of dual generalized order statistics’ concomitants arising from the Sarmanov family
- Residual Inaccuracy Extropy and its properties
- Archimedean ℓ-groups with strong unit: cozero-sets and coincidence of types of ideals