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Constructing the graphs with some specific properties is an important and interesting problem in the field of graph theory. A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to permutation of the colors. In this paper, we give three methods for recursively constructing uniquely 3-colorable graphs. Moreover, we give a simple counterexample on 16 vertices...
Analyzing chromatic number in coloring problem is a tough topic in graph analysis. We focus on the basic theory for a particular type of chromatic number. This will give us insights on the basic topological structure guiding lots of networks in the coming trend of big data era. An adjacent vertex-distinguishing total k-coloring is a proper total k-coloring of a graph G such that for any two adjacent...
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