On the Adjacent Strong Equitable Edge Coloring ofPn∨Pn,Pn∨CnandCn∨Cn

Jun Liu,Qiu Ju Yue,Shu Xia Yao,Chuan Cheng Zhao,Zhi Guo Ren

doi:10.1051/matecconf/20164402033

Abstract

A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different,and the number of edges in any two color classes differ by at most one,which the required minimum number of colors is called the adjacent strong equitable edge chromatic number. In this paper, we discuss the adjacent strong equitable edge coloring of join-graphs about P n ∨ P n , P n ∨ C n and C n ∨ C n .

Highlights

1 Introduction p t 3 and G z C5 (5-cyycle), The coloring problem of graphs is widely applied in practice
(1) If G is a bipartite graph with no isolate edges
Let f be as follows e Mi, f (e) i,i 1,2,n 3

Summary

Conjecture For a connected graph with order

1 Introduction p t 3 and G z C5 (5-cyycle), The coloring problem of graphs is widely applied in practice. Facs (G) d '(G) 2 (2)If G is a k-chromatic graph with no isolate edges, coloring of G, is abbreviated k-SEC, and. Is called the strong edge chromatic number of G. For u, v E(G), C(u) z C(v) , f is called k-adjacent strong edge coloring of G, is abbreviated k-ASEC, and. LEMMA 1 If G is a connected graph with satisfied with Ei E j d 1i, j 1,2,", k f is called the adjacent strong equitable edge coloring of G, and noted by k−ASEECofG, and. Where e Ei , f (e) i(i 1,2,", k), Fc(G) is the aauthore-mail: 527876625@.qq.com This studywas supported by Lanzhou City University Ph.D. Research Fund (21265099,41361013,GS[2013]GHB1084, LZCU-BS2013-09 and LZCU-BS2013-12).

Have a solution y

For f we have