Book ChapterDOI
γ -Chromatic Partition in Planar Graph Characterization
M. Yamuna,A. Elakkiya +1 more
- pp 461-468
Reads0
Chats0
TLDR
In this article, a uniquely colorable graph G whose chromatic partition contains at least one γ-set is characterized as a γ uniquely colourable graph and characterized the planarity of these graphs using the domination number of G.Abstract:
A uniquely colorable graph G whose chromatic partition contains at least one γ-set is termed as a γ-uniquely colorable graph. We characterize the planarity of these graphs using the domination number of G.read more
References
More filters
Journal ArticleDOI
Every planar graph with nine points has a nonplanar complement
TL;DR: In this paper, it is shown that n = 9, verifying a conjecture of J. L. Harary, who stated that n is the least integer n such that every graph G with n points or its complement G is nonplanar.
Journal ArticleDOI
Uniquely colorable graphs
TL;DR: A graph is called uniquely colorable if there is only one partition of its point set into the smallest possible number of color classes as mentioned in this paper, and every homomorphic image of G is also uniquely colourable.
Journal ArticleDOI
A graph and its complement with specified properties. I: Connectivity.
Jin Akiyama,Frank Harary +1 more
TL;DR: In this paper, the conditions under which both a graph G and its complement G¯ possess a specified property were investigated, and all graphs G for which G and G& #175 have connectivity one, (b) have line-connectivity one, and (c) are 2-connected, (d) are forests, (e) are bipartite, (f) are outerplanar and (g) are eulerian.
Journal ArticleDOI
On the Maximum Number of Dominating Classes in Graph Coloring
TL;DR: In this paper, the dominating-c-color number of a graph G is investigated, i.e., the maximum number of color classes that are also dominating when G is colored using colors.