I would like to update the live data by sending 1 set of data point rather than sending whole data series array and old value should get auto deleted.
This can be done starting from sample of the Gallery Dynamic Update
Calling updateOptions after updating the data series.
Here a snipnet showing how to append a new data and delete the oldest one :
var data = [];
var t = new Date();
for (var i = 10; i >= 0; i--) {
var x = new Date(t.getTime() - i * 1000);
data.push([x, Math.random()]);
}
var g = new Dygraph(document.getElementById("graph"), data, {height:200});
window.setInterval(function() {
var x = new Date();
var y = Math.random();
data.shift();
data.push([x, y]);
g.updateOptions( { 'file': data } );
}, 1000);
<script src="https://cdnjs.cloudflare.com/ajax/libs/dygraph/1.1.1/dygraph-combined.js"></script>
<div id="graph" />