So, can any monk would suggest me any better way to write this code that is more robust, with use strict'.

This produces the same output as the original and works with warnings and strict enabled:

Update: fixed an edge case in sub read_file.

#!/usr/bin/perl
use warnings;
use strict;

use GD;


my ( $min1, $max1, $x1, $y1, $lines ) = read_file( 'fwd.stb' );

# Define constants
my $X1start = 50 + 20;               # X-axis
my $Y1start = 300;                   # X-axis
my $X1end   = 450 + $lines - 400;    # X-axis
my $Y1end   = 300;                   # X-axis
my $X2start = 50 + 20;
my $Y2start = 100;
my $X2end   = 50 + 20;
my $Y2end   = 300;

# create a new image
my $im = new GD::Image( $X1end + 50, $Y2end + 100 );

# allocate some colors
my $white = $im->colorAllocate( 255, 255, 255 );
my $green = $im->colorAllocate( 0,   255, 0 );
my $black = $im->colorAllocate( 0,   0,   0 );
my $red   = $im->colorAllocate( 255, 0,   0 );
my $blue  = $im->colorAllocate( 0,   0,   255 );


my $half_lines = int( $lines / 2 );
# set the caption for the graph
$im->string( gdLargeFont, $half_lines - 50, 20, 'ENERGY GRAPH', $black
+ );

# draw the y-axis & x-axis
$im->line( $X2start, $Y2start, $X2end, $Y2end, $black );
$im->line( $X1start, $Y1start, $X1end, $Y1end, $black );

# set the caption for x-axis and y-axis
$im->string(   gdLargeFont, $half_lines - 50, 335, 'NUCLEOTIDE POSITIO
+N', $black );
$im->stringUp( gdLargeFont, 5, 260, 'FREE ENERGY(delta G)', $black );

$im->string( gdSmallFont, $half_lines + 100, 20, ' Genomic  Sequence -
+------', $red );
$im->string( gdSmallFont, $half_lines + 100, 40, ' Shuffled Sequence -
+------', $blue );


my ( $min2, $max2, $x2, $y2 ) = read_file( 'total_shuffle.stb' );


my $min = $min1 <= $min2 ? $min1 : $min2;
my $max = $max1 >= $max2 ? $max1 : $max2;

graph( $x1, $y1, $min, $max );


open my $DISPLAY, '|-:raw', 'display', '-' or die "Cannot open pipe to
+ 'display' $!";
print $DISPLAY $im->png;
close $DISPLAY or warn $! ? "Error closing 'display' pipe: $!" : "Exit
+ status $? from 'display'";

exit 0;


sub read_file {
    my $file_name = shift;

    open my $fh, '<', $file_name or die "Cannot open '$file_name' $!";

    my ( $min, $max, @x, @y );
    while ( <$fh> ) {
        my @value = split;
        push @x, $value[ 0 ] - 7;
        push @y, $value[ 1 ];

        if ( @y > 1 ) {
            $max = $y[ -1 ] if $max < $y[ -1 ];
            $min = $y[ -1 ] if $min > $y[ -1 ];
            }
        elsif ( @y == 1 ) {
            $min = $max = $y[ -1 ];
            }
        }

    return $min, $max, \@x, \@y, $.;
    }

sub graph {
    my ( $x_ref, $y_ref, $minEnergy, $maxEnergy ) = @_;

    # Scaling the values
    my $Yscale = ( $Y2end - $Y2start ) / ( abs( $minEnergy ) - abs( $m
+axEnergy ) );

    my $scale = ( $minEnergy - $maxEnergy ) / 5;

    my $incEnergy = $maxEnergy;
    while ( $incEnergy > $minEnergy ) {   ##### Prob loop####

        my $x1 = $X1start - 2;
        my $y1 = int( ( ( abs( $incEnergy ) - abs( $maxEnergy ) ) * $Y
+scale ) + $Y2start );
        my $x2 = $X1start + 2;

        $im->line( $x1, $y1, $x2, $y1, $black );
        my $displayEnergy = sprintf '%2.1f', $incEnergy;
        $im->string( gdSmallFont, $x1 - 35, $y1 - 10, $displayEnergy, 
+$black );
        $incEnergy = $incEnergy + $scale;
        }

    # mark 10 points on the position axis
    my $posSkip = int( @$x_ref / 10 );
    # If the length of the fragment is lesser than the x-axis

    my $skipPixel = ( $X1end - $X1start ) / @$x_ref;

    my $count;
    for my $i ( 0 .. $#$x_ref - 1 ) {
        my $x1 = int( $i * $skipPixel + $X1start );
        my $y1 = int( ( abs( $y_ref->[ $i ] ) - abs( $maxEnergy ) ) * 
+$Yscale + $Y2start );
        my $x2 = int( ( $i + 1 ) * $skipPixel + $X1start );
        my $y2 = int( ( abs( $y_ref->[ $i + 1 ] ) - abs( $maxEnergy ) 
+) * $Yscale + $Y2start );

        $im->line( $x1, $y1, $x2, $y2, $red );
        $count++;

        if ( $count == $posSkip ) {
            $x1 = int( $i * $skipPixel + $X1start );
            $y1 = $Y1end - 2;
            $x2 = int( $i * $skipPixel + $X1start );
            $y2 = $Y1end + 2;

            $im->line( $x1, $y1, $x2, $y2, $black );
            $im->string( gdSmallFont, $x1, $y1 + 10, $i + 1, $black );
            $count = 0;
            }
        }
    }

__END__
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