Hamiltonian Paths in Some Classes of Grid Graphs

<table>(a) A rectangular grid graph <svg height="13.45" id="M49" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 59.862499 13.45" width="59.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑅</tspan>
<tspan style="font-size: 12.50px; " x="9.2522202" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="13.415719" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="19.667219" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="25.918718" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="31.119967" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="37.371468" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="43.622967" y="0">)</tspan>
</text>
</g>
</g>
</svg>, (b) an <svg height="10.325" id="M50" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐿</tspan>
</text>
</g>
</g>
</svg>-alphabet grid graph <svg height="13.45" id="M51" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 43.737499 13.45" width="43.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐿</tspan>
<tspan style="font-size: 12.50px; " x="8.8521242" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="13.015623" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="19.267122" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="24.46837" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="30.719872" y="0">)</tspan>
</text>
</g>
</g>
</svg>, (c) an <svg height="10.6125" id="M52" style="vertical-align:-0.15048pt" version="1.1" viewbox="0 0 11.8625 10.6125" width="11.8625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6125)">
<g transform="translate(72,-63.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.71)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐶</tspan>
</text>
</g>
</g>
</svg>-alphabet grid graph <svg height="13.45" id="M53" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 43.162498 13.45" width="43.162498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐶</tspan>
<tspan style="font-size: 12.50px; " x="8.389513" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="12.553012" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="18.804512" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="24.00576" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="30.257259" y="0">)</tspan>
</text>
</g>
</g>
</svg>, (d) an <svg height="10.325" id="M54" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan>
</text>
</g>
</g>
</svg>-alphabet grid graph <svg height="13.45" id="M55" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 42.337502 13.45" width="42.337502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan>
<tspan style="font-size: 12.50px; " x="7.7268538" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="11.890353" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="18.141853" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="23.343102" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="29.594601" y="0">)</tspan>
</text>
</g>
</g>
</svg>, (e) an <svg height="10.325" id="M56" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.225 10.325" width="12.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
</text>
</g>
</g>
</svg>-alphabet grid graph <svg height="13.45" id="M57" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 43.837502 13.45" width="43.837502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
<tspan style="font-size: 12.50px; " x="8.9271421" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="13.090641" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="19.34214" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="24.543388" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="30.794889" y="0">)</tspan>
</text>
</g>
</g>
</svg>.</table>

Journal of Applied Mathematics

Hamiltonian Paths in Some Classes of Grid Graphs

Figure 1