Energy-Aware Topology Evolution Model with Link and Node Deletion in Wireless Sensor Networks

<table>The average degree of neighboring node <svg height="16.450001" id="M179" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 41.5625 16.450001" width="41.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D458"></use></g>
<g transform="matrix(.012,-0,0,-.012,8.612,16.25)"><path d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" id="x1D45B"></path></g><g transform="matrix(.012,-0,0,-.012,14.586,16.25)"><use xlink:href="#x1D45B"></use></g>
<g transform="matrix(.017,-0,0,-.017,21.188,12.162)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,27.069,12.162)"><use xlink:href="#x1D458"></use></g><g transform="matrix(.017,-0,0,-.017,35.619,12.162)"><use xlink:href="#x29"></use></g>
</svg> obtained by simulations for three kinds of node energy distribution <svg height="16.625" id="M180" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 31.7875 16.625" width="31.7875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x1D70C"></use></g><g transform="matrix(.017,-0,0,-.017,9.225,12.138)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,15.106,12.138)"><use xlink:href="#x1D438"></use></g><g transform="matrix(.017,-0,0,-.017,25.85,12.138)"><use xlink:href="#x29"></use></g>
</svg>, where <svg height="11.075" id="M181" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 41.112499 11.075" width="41.112499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.8)"><use xlink:href="#x1D45A"></use></g><g transform="matrix(.017,-0,0,-.017,18.183,10.8)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,32.887,10.8)"><use xlink:href="#x34"></use></g>
</svg>, <svg height="15.2875" id="M182" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 49.825001 15.2875" width="49.825001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><use xlink:href="#x1D45D"></use></g><g transform="matrix(.017,-0,0,-.017,14.851,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,29.555,10.862)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,37.715,10.862)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,41.59,10.862)"><use xlink:href="#x35"></use></g>
</svg>.</table>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Energy-Aware Topology Evolution Model with Link and Node Deletion in Wireless Sensor Networks 