It is well known that a simple graph
930&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=a247e0a9980bc1682b15ce3bc33933e4" title="Click to view the MathML source">C⁎-algebra is either AF or purely infinite. In this paper, we address the question of whether this is the case for labeled graph
930&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=a247e0a9980bc1682b15ce3bc33933e4" title="Click to view the MathML source">C⁎-algebras which include all graph
930&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=a247e0a9980bc1682b15ce3bc33933e4" title="Click to view the MathML source">C⁎-algebras and Matsumoto algebras of subshifts. There have been various
930&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=a247e0a9980bc1682b15ce3bc33933e4" title="Click to view the MathML source">C⁎-algebra constructions associated with subshifts and some of them are known to have the crossed products
930&_mathId=si2.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=c97f10e645e60962858537ba602a985f" title="Click to view the MathML source">C(X)×TZ of Cantor minimal subshifts
930&_mathId=si3.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=032d0d34d53a676c98b6287192182372" title="Click to view the MathML source">(X,T) as their quotient algebras.
We show that such a simple crossed product 930&_mathId=si2.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=c97f10e645e60962858537ba602a985f" title="Click to view the MathML source">C(X)×TZ can be realized as a labeled graph 930&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=a247e0a9980bc1682b15ce3bc33933e4" title="Click to view the MathML source">C⁎-algebra. Since this 930&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=a247e0a9980bc1682b15ce3bc33933e4" title="Click to view the MathML source">C⁎-algebra is known to be an 930&_mathId=si5.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=53e66d0fd1722c9c0afe99c63d4aabf1" title="Click to view the MathML source">AT algebra and has 930&_mathId=si6.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=09168ef6d11c910ecdd7674464319ac4" title="Click to view the MathML source">Z as its 930&_mathId=si7.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=a0c9639afd62171e240f27d2c7af500c" title="Click to view the MathML source">K1-group, our result provides a family of simple finite non-AF unital labeled graph 930&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304930&_rdoc=1&_issn=0022247X&md5=a247e0a9980bc1682b15ce3bc33933e4" title="Click to view the MathML source">C⁎-algebras.