On the adjacent vertex-distinguishing equitable edge coloring of graphs

2013 ◽  
Vol 29 (3) ◽  
pp. 615-622 ◽  
Author(s):  
Jing-wen Li ◽  
Cong Wang ◽  
Zhi-wen Wang
Keyword(s):  
Edge Coloring ◽  
Adjacent Vertex ◽  
Equitable Edge Coloring

A STUDY ON FUZZY EQUITABLE EDGE COLORING OF WHEEL RELATED GRAPHS

2020 ◽  
Vol 9 (11) ◽  
pp. 9311-9317
Author(s):  
K. Sivaraman ◽  
R.V. Prasad
Keyword(s):  
Edge Coloring ◽  
Graph Labeling ◽  
Equitable Edge Coloring

Equitable edge coloring is a kind of graph labeling with the following restrictions. No two adjacent edges receive same label (color). and number of edges in any two color classes differ by at most one. In this work we are going to present the Fuzzy equitable edge coloring of some wheel related graphs.

Adjacent vertex distinguishing edge coloring of planar graphs without 3-cycles

2020 ◽  
Vol 12 (04) ◽  
pp. 2050035
Author(s):  
Danjun Huang ◽  
Xiaoxiu Zhang ◽  
Weifan Wang ◽  
Stephen Finbow
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Edge Coloring ◽  
Discrete Math ◽  
Adjacent Vertex ◽  
Chromatic Index ◽  
Proper Edge Coloring ◽  
Minimum Number

The adjacent vertex distinguishing edge coloring of a graph [Formula: see text] is a proper edge coloring of [Formula: see text] such that the color sets of any pair of adjacent vertices are distinct. The minimum number of colors required for an adjacent vertex distinguishing edge coloring of [Formula: see text] is denoted by [Formula: see text]. It is observed that [Formula: see text] when [Formula: see text] contains two adjacent vertices of degree [Formula: see text]. In this paper, we prove that if [Formula: see text] is a planar graph without 3-cycles, then [Formula: see text]. Furthermore, we characterize the adjacent vertex distinguishing chromatic index for planar graphs of [Formula: see text] and without 3-cycles. This improves a result from [D. Huang, Z. Miao and W. Wang, Adjacent vertex distinguishing indices of planar graphs without 3-cycles, Discrete Math. 338 (2015) 139–148] that established [Formula: see text] for planar graphs without 3-cycles.

On the Adjacent Vertex Distinguishing Proper Edge Colorings of Several Classes of Complete 5-Partite Graphs

2013 ◽  
Vol 333-335 ◽  
pp. 1452-1455
Author(s):  
Chun Yan Ma ◽  
Xiang En Chen ◽  
Fang Yang ◽  
Bing Yao
Keyword(s):  
Chromatic Number ◽  
Edge Coloring ◽  
Adjacent Vertex ◽  
Chromatic Numbers ◽  
Edge Colorings ◽  
Proper Edge Coloring ◽  
Minimum Number

A proper $k$-edge coloring of a graph $G$ is an assignment of $k$ colors, $1,2,\cdots,k$, to edges of $G$. For a proper edge coloring $f$ of $G$ and any vertex $x$ of $G$, we use $S(x)$ denote the set of thecolors assigned to the edges incident to $x$. If for any two adjacent vertices $u$ and $v$ of $G$, we have $S(u)\neq S(v)$,then $f$ is called the adjacent vertex distinguishing proper edge coloring of $G$ (or AVDPEC of $G$ in brief). The minimum number of colors required in an AVDPEC of $G$ is called the adjacent vertex distinguishing proper edge chromatic number of $G$, denoted by $\chi^{'}_{\mathrm{a}}(G)$. In this paper, adjacent vertex distinguishing proper edge chromatic numbers of several classes of complete 5-partite graphs are obtained.

Upper bounds for adjacent vertex-distinguishing edge coloring

2017 ◽  
Vol 35 (2) ◽  
pp. 454-462 ◽  
Author(s):  
Junlei Zhu ◽  
Yuehua Bu ◽  
Yun Dai
Keyword(s):  
Edge Coloring ◽  
Upper Bounds ◽  
Adjacent Vertex

An equitable edge coloring of some classes of product of graphs

2020 ◽  
Vol 8 (4) ◽  
pp. 1354-1357
Author(s):  
Manikandan K. ◽  
Moidhen Aliyar S. ◽  
Manimaran S.
Keyword(s):  
Edge Coloring ◽  
Product Of Graphs ◽  
Equitable Edge Coloring

FUZZY EQUITABLE EDGE COLORING OF SOME SIMPLE GRAPHS

2020 ◽  
Vol 9 (11) ◽  
pp. 9303-9310
Author(s):  
K. Sivaraman ◽  
R.V. Prasad
Keyword(s):  
Edge Coloring ◽  
Simple Graphs ◽  
Equitable Edge Coloring

In our earlier works, we have discussed about the equitable edge coloring of various classes of some simple graphs (or crisp graphs). In this Paper we are going to state and discuss the Fuzzy equitable edge coloring of some classes of simple graphs.

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