Open AccessDevelopment of Management System for eduroam Database Updated Specification
Author(s) -
Artur Petrosyan,
Gurgen S. Petrosyan
Publication year - 2021
Publication title -
mathematical problems of computer science
Language(s) - English
Resource type - Journals
eISSN - 2738-2788
pISSN - 2579-2784
DOI - 10.51408/1963-0070
Subject(s) - combinatorics , edge coloring , palette (painting) , vertex (graph theory) , graph , cartesian product , windmill graph , mathematics , discrete mathematics , computer science , graph power , line graph , operating system
Given a proper edge coloring α of a graph G, we define the palette SG(ν, α) of a vertex ν ∈ V (G) as the set of all colors appearing on edges incident to ν. The palette index š(G) of G is the minimum number of distinct palettes occurring in a proper edge coloring of G. The windmill graph Wd(n, k) is an undirected graph constructed for k ≥ 2 and n ≥ 2 by joining n copies of the complete graph Kk at a shared universal vertex. In this paper, we determine the bound on the palette index of Cartesian products of complete graphs and simple paths. We also consider the problem of determining the palette index of windmill graphs. In particular, we show that for any positive integers n, k ≥ 2, š(Wd(n, 2k)) = n + 1.