2014/10/30 by Johan Kok, Kok, Johan, C Susanth +2
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1410.8328
10 pages. To be submitted to the Pioneer Journal of Mathematics and Mathematical Sciences
arxiv created 2014/10/30 · openalex publication_date 2014/10/30 · arxiv updated 2014/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kok et.al. [7] introduced Jaco Graphs (order 1). In this essay we present a recursive formula to determine the independence number α(Jn(1)) = |\Bbb I| with, \Bbb I = \vi,j| v1 = v1,1 ∈ \Bbb I and vi = vi,j =v_(d+(vm, (j-1)) + m +1)\. We also prove that for the Jaco Graph, Jn(1), n ∈ \Bbb N with the prime Jaconian vertex vi the chromatic number, χ(Jn(1)) is given by: χ(Jn(1)) \begincases = (n-i) + 1, if and only if the edge vivn exists,
= n-i otherwise. \endcases We further our exploration in respect of domination numbers, bondage numbers and declare the concept of the murtage number of a simple connected graph G, denoted m(G). We conclude by proving that for any Jaco Graph Jn(1), n ∈ \Bbb N we have that 0 ≤ m(Jn(1)) ≤ 3.