| مستخلص: |
In this paper, we show that with the exception of the graph C 12 (1 , 3) , which we prove to be Type 2 , all members of the following three infinite families of 4-regular circulant graphs: C n (2 k , 3) , k ≥ 1 and n = (8 μ + 6 λ) k , for nonnegative integers μ and λ ; C 3 n (1 , 3) , for n ≥ 3 and n ≠ 4 ; and C 3 λ p (1 , p) , for λ ≥ 1 and p multiple of 3 are Type 1. The last two results are what is expected whether the Khennoufa and Togni's conjecture is true, which states that 4-regular circulant graphs C n (1 , k) are Type 1 with 1 < k < n 2 , but a finite number of Type 2 graphs. It is known that if a graph G is Type 1 , then it is conformable. Furthermore, we introduce a relationship between the conformability problem and the equitable vertex coloring problem, by showing infinite families for which any equitable (Δ + 1) -vertex coloring is conformable. In this context, we exhibit the infinite conformable graph family C (2 q + 1) n (d 1 , ... , d q) , n , q positive integers, containing C 5 n (d 1 , d 2) , which in turns, comprises one fifth of all 4-regular circulant graphs. [ABSTRACT FROM AUTHOR] |
