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Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 9
Discrete Mathematics, 2019For a simple graph $G$, an adjacent vertex distinguishing (or AVD) total $k$-coloring is a proper total $k$-coloring of $G$ such that any two adjacent vertices have different color sets; a color set for vertex $v$ consisting of the color of $v$ and the colors of its incidence edges.
Jie Hu +4 more
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Adjacent vertex distinguishing total coloring of planar graphs with large maximum degree
SCIENTIA SINICA Mathematica, 2012An 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 needed for an adjacent vertex distinguishing total coloring of G is denoted by χa′′( G ).
WeiFan WANG, DanJun HUANG
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The Smarandachely Adjacent Vertex Distinguishing E-Total Coloring of some Join Graphs
Applied Mechanics and Materials, 2013Using the analysis method and the function of constructing the Smarandachely adjacent vertex distinguishing E-total coloring function, the Smarandachely adjacent vertex distinguishing E-total coloring of join graphs are mainly discussed, and the Smarandachely adjacent vertex distinguishing E-total chromatic number of join graph are obtained.
Mu Chun Li, Shuang Li Wang, Li Li Wang
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The Smarandachely adjacent-vertex distinguishing total coloring of two kind of 3-regular graphs
2010 3rd International Conference on Biomedical Engineering and Informatics, 2010The Smarandachely adjacent-vertex distinguishing total coloring of graphs is a proper k-total coloring such that every adjacent vertex coloring set not embrace each other, the minimal number k is denoted the Smarandachely adjacent-vertex distinguishing total coloring chromatic number of graphs.
Jingwen Li +3 more
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Applied Mechanics and Materials, 2013
υυυLet G be a simple graph, k be a positive integer, f be a mapping from V(G)∪E(G) to {1,2,...,k} . If ∀uv∈E(G) , we have f(u)≠f(v) , f(u)≠f(uv),f(v)≠f(uv) , C(u)≠C(v), where C(u)={f(u)}∪{f(uv)|uv∈E(G)}. Then f is called the adjacent vertex distinguishing E-total coloring of G.
Mu Chun Li, Li Zhang
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υυυLet G be a simple graph, k be a positive integer, f be a mapping from V(G)∪E(G) to {1,2,...,k} . If ∀uv∈E(G) , we have f(u)≠f(v) , f(u)≠f(uv),f(v)≠f(uv) , C(u)≠C(v), where C(u)={f(u)}∪{f(uv)|uv∈E(G)}. Then f is called the adjacent vertex distinguishing E-total coloring of G.
Mu Chun Li, Li Zhang
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Advanced Materials Research, 2012
Let G(V,E) be a simple graph, k be a positive integer, f be a mapping from V(G)E(G) to 1,2,...k. If uvE(G), we have f(u)≠f(v),f(u)≠f(uv) ,f(v)≠f(uv) ,C(u)≠C(v) , where C(u). Then f is called the adjacent vertex-distinguishing E-total coloring of G. The number is called the adjacent vertex –distinguishing E-total chromatic number of G.
Mu Chun Li, Li Zhang
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Let G(V,E) be a simple graph, k be a positive integer, f be a mapping from V(G)E(G) to 1,2,...k. If uvE(G), we have f(u)≠f(v),f(u)≠f(uv) ,f(v)≠f(uv) ,C(u)≠C(v) , where C(u). Then f is called the adjacent vertex-distinguishing E-total coloring of G. The number is called the adjacent vertex –distinguishing E-total chromatic number of G.
Mu Chun Li, Li Zhang
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The Smarandachely adjacent vertex distinguishing E-total coloring of a number of 3-regular graphs
2013 2nd International Symposium on Instrumentation and Measurement, Sensor Network and Automation (IMSNA), 2013Application of analytic method and Constructing the Smarandachely adjacent vertex distinguishing E-total coloring function, the Smarandachely adjacent vertex distinguishing E-total coloring of two kinds of 3-regular graphs are mainly discussed, and the Smarandachely adjacent vertex distinguishing E-total chromatic number of join graph are obtained. The
Muchun Li, Shuangli Wang
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2007
The graph obtained by the famous Mycielski's construction is called the Mycielski graph. This paper focuses on the relation between the basic graphs and two classes of constructed graphs on the (adjacent) vertex-distinguishing total coloring. And some sufficient conditions with which the Mycielski graphs and the Cartesian product graphs satisfy the ...
Yanli Sun, Lei Sun
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The graph obtained by the famous Mycielski's construction is called the Mycielski graph. This paper focuses on the relation between the basic graphs and two classes of constructed graphs on the (adjacent) vertex-distinguishing total coloring. And some sufficient conditions with which the Mycielski graphs and the Cartesian product graphs satisfy the ...
Yanli Sun, Lei Sun
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On the total vertex irregularity strength of trees
Discrete Mathematics, 2010Nurdin, Edy Tri Baskoro, Anm Salman
exaly
Far East Journal of Mathematical Sciences (FJMS), 2019
R. Ezhilarasi, K. Thirusangu
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R. Ezhilarasi, K. Thirusangu
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