Adjacent Vertex Distinguishing I-total Coloring of Outerplanar Graphs

GUO Jing, CHEN Xiang-en

doi:10.13371/j.cnki.chin.q.j.m.2017.04.005

Chinese Quarterly Journal of Mathematics >

2017 , Vol. 32 >Issue 4: 382 - 394

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.04.005

Adjacent Vertex Distinguishing I-total Coloring of Outerplanar Graphs

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College of Mathematics and Statistics, Northwest Normal University

GUO Jing(1988-), male, native of Lanzhou, Gansu, a lecturer of Northwest Normal University, M.S.D., engages in graph theory with applications.

Received date: 2015-06-13

Online published: 2020-10-20

Supported by

Supported by the National Natural Science Foundation of China(61163037,61163054,61363060)；

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Abstract

Let G be a simple graph with no isolated edge. An Ⅰ-total coloring of a graph G is a mapping φ : V(G) ∪ E(G) → {1, 2, ···, k} such that no adjacent vertices receive the same color and no adjacent edges receive the same color. An Ⅰ-total coloring of a graph G is said to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, we have C_φ(u) = C_φ(v), where C_φ(u) denotes the set of colors of u and its incident edges. The minimum number of colors required for an adjacent vertex distinguishing Ⅰ-total coloring of G is called the adjacent vertex distinguishing Ⅰ-total chromatic number, denoted by χ_at~i(G).In this paper, we characterize the adjacent vertex distinguishing Ⅰ-total chromatic number of outerplanar graphs.

Key words： adjacent vertex distinguishing I-total coloring; outerplanar graphs; maximum degree

Cite this article

GUO Jing, CHEN Xiang-en . Adjacent Vertex Distinguishing I-total Coloring of Outerplanar Graphs[J]. Chinese Quarterly Journal of Mathematics, 2017 , 32(4) : 382 -394 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.04.005

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