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The 3-arc graph of <jats:inline-formula>\n                     <p:math xmlns:p=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <p:mi>H<\/p:mi>\n                     <\/p:math>\n                  <\/jats:inline-formula> is the graph with vertex set all arcs of <jats:inline-formula>\n                     <r:math xmlns:r=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\">\n                        <r:mi>H<\/r:mi>\n                     <\/r:math>\n                  <\/jats:inline-formula> and edge set containing all edges joining <jats:inline-formula>\n                     <t:math xmlns:t=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\">\n                        <t:mi>x<\/t:mi>\n                        <t:mi>y<\/t:mi>\n                     <\/t:math>\n                  <\/jats:inline-formula> and <jats:inline-formula>\n                     <v:math xmlns:v=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\">\n                        <v:mi>v<\/v:mi>\n                        <v:mi>w<\/v:mi>\n                     <\/v:math>\n                  <\/jats:inline-formula> whenever <jats:inline-formula>\n                     <x:math xmlns:x=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\">\n                        <x:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <x:mrow>\n                              <x:mi>y<\/x:mi>\n                              <x:mo>,<\/x:mo>\n                              <x:mi>x<\/x:mi>\n                              <x:mo>,<\/x:mo>\n                              <x:mi>v<\/x:mi>\n                              <x:mo>,<\/x:mo>\n                              <x:mi>w<\/x:mi>\n                           <\/x:mrow>\n                        <\/x:mfenced>\n                     <\/x:math>\n                  <\/jats:inline-formula> is a 3-arc of <jats:inline-formula>\n                     <cb:math xmlns:cb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\">\n                        <cb:mi>H<\/cb:mi>\n                     <\/cb:math>\n                  <\/jats:inline-formula>. A Hamilton cycle is a closed path meeting each vertex of a graph. A graph <jats:inline-formula>\n                     <eb:math xmlns:eb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\">\n                        <eb:mi>H<\/eb:mi>\n                     <\/eb:math>\n                  <\/jats:inline-formula> including a Hamilton cycle is called Hamiltonian and <jats:inline-formula>\n                     <gb:math xmlns:gb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\">\n                        <gb:mi>H<\/gb:mi>\n                     <\/gb:math>\n                  <\/jats:inline-formula> has a Hamiltonian decomposition provided its edge set admits a partition into disjoint Hamilton cycles (possibly with a single perfect matching). The current paper proves that every connected 3-arc graph consists of more than one Hamilton cycle. Since the 3-arc graph of a cubic graph is 4-regular, it further proves that each 3-arc graph of a cubic graph in a certain family has a Hamiltonian decomposition.<\/jats:p>","DOI":"10.1155\/2022\/5837405","type":"journal-article","created":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T02:59:19Z","timestamp":1651201159000},"page":"1-6","source":"Crossref","is-referenced-by-count":0,"title":["On Hamiltonian Decomposition Problem of 3-Arc Graphs"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0494-4741","authenticated-orcid":true,"given":"Guangjun","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematics, Zunyi Normal University, Zunyi, Guizhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8990-9610","authenticated-orcid":true,"given":"Qiang","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Yangzhou University, Yangzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7019-4195","authenticated-orcid":true,"given":"Zuosong","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Management, Qufu Normal University, Rizhao, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.08.010"},{"key":"2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84628-970-5","volume-title":"Graph Theory","author":"J. 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