[PDF][PDF] Adjacent vertex distinguishing total coloring of graphs with lower average degree
W Wang, Y Wang - Taiwanese Journal of Mathematics, 2008 - projecteuclid.org
W Wang, Y Wang
Taiwanese Journal of Mathematics, 2008•projecteuclid.orgAn adjacent vertex distinguishing total coloring of a graph $ G $ is a proper total coloring of $
G $ such that any pair of adjacent vertices are incident to distinct sets of colors. The
minimum number of colors required for an adjacent vertex distinguishing total coloring of $ G
$ is denoted by $\chi''_ {a}(G) $. Let mad $(G) $ and $\Delta (G) $ denote the maximum
average degree and the maximum degree of a graph $ G $, respectively. In this paper, we
prove the following results:(1) If $ G $ is a graph with mad $(G)\lt 3$ and $\Delta (G)\ge 5 …
G $ such that any pair of adjacent vertices are incident to distinct sets of colors. The
minimum number of colors required for an adjacent vertex distinguishing total coloring of $ G
$ is denoted by $\chi''_ {a}(G) $. Let mad $(G) $ and $\Delta (G) $ denote the maximum
average degree and the maximum degree of a graph $ G $, respectively. In this paper, we
prove the following results:(1) If $ G $ is a graph with mad $(G)\lt 3$ and $\Delta (G)\ge 5 …
An adjacent vertex distinguishing total coloring of a graph is a proper total coloring of such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing total coloring of is denoted by . Let mad and denote the maximum average degree and the maximum degree of a graph , respectively. In this paper, we prove the following results: (1) If is a graph with mad and , then , and if and only if contains two adjacent vertices of maximum degree; (2) If is a graph with mad and , then ; (3) If is a graph with mad and , then .
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