NDLI: Some properties onf-edge covered critical graphs

Content Provider	Springer Nature Link
Author	Wang, Jihui Hou, Jianfeng Liu, Guizhen
Copyright Year	2007
Abstract	LetG(V, E) be a simple graph, and letf be an integer function onV with 1 ≤f(v) ≤d(v) to each vertexv ∈V. An f-edge cover-coloring of a graphG is a coloring of edge setE such that each color appears at each vertexv ∈V at leastf(v) times. Thef-edge cover chromatic index ofG, denoted by χ′$_{ fc }$ (G), is the maximum number of colors such that anf-edge cover-coloring ofG exists. Any simple graphG has anf-edge cover chromatic index equal to δ$_{f}$ or δ$_{ f }$ - 1, where $$\delta _f = \mathop {\min }\limits_{\upsilon \in V} \{ \left\lfloor {\frac{{d(v)}}{{f(v)}}} \right\rfloor \} $$ . LetG be a connected and not complete graph with χ′$_{ fc }$(G)=δ$_{ f-1}$, if for eachu, v ∈V and e =uv ∉E, we have ÷$_{ fc }$(G + e) > ÷$_{ fc }$(G), thenG is called anf-edge covered critical graph. In this paper, some properties onf-edge covered critical graph are discussed. It is proved that ifG is anf-edge covered critical graph, then for eachu, v ∈V and e =uv ∉E there existsw ∈ {u, v } withd(w) ≤ δ$_{ f }$(f(w) + 1) - 2 such thatw is adjacent to at leastd(w) - δ$_{ f }$ + 1 vertices which are all δ$_{ f }$-vertex inG.
Starting Page	357
Ending Page	366
Page Count	10
File Format	PDF
ISSN	15985865
Journal	Journal of Applied Mathematics and Computing
Volume Number	24
Issue Number	1-2
e-ISSN	18652085
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	f-edge cover-coloring f-edge covered critical graph f-edge cover chromatic index Coloring of graphs and hypergraphs Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theory of Computation Mathematics of Computing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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