Total Irregularity and fₜ-Irregularity of Linear Jaco Graphs

الأصل · EN

Total irregularity of a simple undirected graph G is defined to be irrₜ(G) = 1/2∑ᵤ, ᵥ ∈ ᵥ₍G₎|d(u) - d(v)|. See Abdo and Dimitrov [2]. We allocate the Fibonacci weight, fᵢ to a vertex vⱼ of a simple connected graph, if and only if d(vⱼ) = i and define the total fibonaccian irregularity or fₜ-irregularity denoted firrₜ(G) for brevity, as: firrₜ(G) = ∑ᵢ₌₁ⁿ⁻¹∑ⱼ₌ᵢ₊₁ⁿ|fᵢ - fⱼ|. The concept of an edge-joint is also introduced to be the simple undirected graph obtained from two simple undirected graphs G and H by linking the edge vuᵥ ∈ ᵥ₍G₎, ᵤ ∈ ᵥ₍ₕ₎. This paper presents results for the undirected underlying graphs of Jaco Graphs, Jₙ(x). Finally we pose an open problem with regards to firrₜ±(G).