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Use an Add shader to combine a Transparent and an Emission shader.

The inclusion of the Transparent shader (set to 100% white) in this way will result in the mesh being fully transparent regardless of the intensity of the emission. ie, it won't cast a shadow and will be invisible apart from the light it emits.

@lemon kindly provided a comparison of various methods with varying emission :

From left to right...

1. Emission shader only

2. Transparent and Emission combined with Add shader

3. Transparent mixed with Emission

4. Transparent mixed with combined Emission/Transparent

1 and 3 produce shadows (and 1, obviously, turns black so is really not good). 2 and 4 don't produce shadows and are fully transparent - the only difference being that 4 fades at a different rate - mostly due to the Mix factor and the emission strength combining to affect the brightness non-linearly.

Use an Add shader to combine a Transparent and an Emission shader.

The inclusion of the Transparent shader (set to 100% white) in this way will result in the mesh being fully transparent regardless of the intensity of the emission. ie, it won't cast a shadow and will be invisible apart from the light it emits.

@lemon kindly provided a comparison of various methods with varying emission :

From left to right...

1. Emission shader only

2. Transparent and Emission combined with Add shader (the one described at the start of this answer)

3. Transparent mixed with Emission

4. Transparent mixed with combined Emission/Transparent

1 and 3 produce shadows (and 1, obviously, turns black so is really not good). 2 and 4 don't produce shadows and are fully transparent - the only difference being that 4 fades at a different rate - mostly due to the Mix factor and the emission strength combining to affect the brightness non-linearly.

For a linearly varying emission with no shadow, number '2' seems the best solution.

Use an Add shader to combine a Transparent and an Emission shader.

The inclusion of the Transparent shader (set to 100% white) in this way will result in the mesh being fully transparent regardless of the intensity of the emission. ie, it won't cast a shadow and will be invisible apart from the light it emits.

Use an Add shader to combine a Transparent and an Emission shader.

The inclusion of the Transparent shader (set to 100% white) in this way will result in the mesh being fully transparent regardless of the intensity of the emission. ie, it won't cast a shadow and will be invisible apart from the light it emits.

@lemon kindly provided a comparison of various methods with varying emission :

From left to right...

1. Emission shader only

2. Transparent and Emission combined with Add shader

3. Transparent mixed with Emission

4. Transparent mixed with combined Emission/Transparent

1 and 3 produce shadows (and 1, obviously, turns black so is really not good). 2 and 4 don't produce shadows and are fully transparent - the only difference being that 4 fades at a different rate - mostly due to the Mix factor and the emission strength combining to affect the brightness non-linearly.

Use an Add shader to combine a Transparent and Emission shaders.

The inclusion of the Transparent shader in this way will result in it being fully transparent regardless of the intensity of the emission.

Use an Add shader to combine a Transparent and an Emission shader.

The inclusion of the Transparent shader (set to 100% white) in this way will result in the mesh being fully transparent regardless of the intensity of the emission. ie, it won't cast a shadow and will be invisible apart from the light it emits.