After we have eaten... the maximum blood supply is transferred towards the digestive system so that digestion is done, and therefore the brain to does not get adequate blood supply. Am I right about this?
This is a very, very common myth, but it is a myth. Because blood flow and oxygen delivery to the brain is critical for survival, cerebral circulation is one of the most tightly regulated systems in the body. Blood is not shunted from the brain to the gut for digestion.
In a normal physiological state, total blood flow to the brain is remarkably constant due in part to the prominent contribution of large arteries to vascular resistance.
Eating, sleeping, walking, etc. are all normal physiological states. If we had blood shunted away from our brains after eating, we'd literally collapse after every meal.
In normotensive adults, cerebral blood flow is maintained at ~50 mL per 100 g of brain tissue per minute, provided CPP is in the range of ~60 to 160 mmHg.
As eating alone doesn't normally cause our blood pressure to rise or fall, cerebral perfusion is constant regardless of what is or isn't in our digestive systems.
Blood flow to the gastrointestinal system (or GI tract) is also regulated, but the flow varies widely:
Estimates of blood flow (in ml /min × 100 g) to the quiescent gastrointestinal tract of dogs and cats range from 15 to 100 for the stomach, 35–120 for the small intestine, and 10–74 for the colon. Somewhat lower values for resting blood flow to the stomach, small intestine, and colon have been reported for man.
So, the basic answer is that, yes, blood flow to the gastrointestinal tract varies, but blood is not shunted from the brain in favor of the GI tract.
So why do we get sleepy after a meal?
Sleepiness after a meal is caused by the level of peptides in your brain called orexins (aka hypocretins).
In 1998, two groups of researchers simultaneously discovered 2 small neuropeptide hormones that regulate, among other things, wakefulness and feeding behavior.
One group discovered them while searching for molecules that could bind to "orphan" receptors, that is, a brain receptor with an unknown "binding" molecule (called a ligand). They found that the prohormone prepro-orexin was found in a very small area of the hypothalamus which had been implicated in the regulation of feeding behavior and energy homeostasis; this suggested the possibility that the neuropeptides might be involved in the regulation of food intake. When administered into free-feeding rats' brains, one of these peptides (orexin A/hypocretin 1) stimulated food consumption in a dose-dependent manner (with attention to light and dark periods, i.e. the circadian rhythm), with a lower dose increasing rat feeding about 2-fold, and the higher dose inducing a 3+-fold increase in feeding compared to rats injected with a solution without the peptide (the other stimulated feeding to a lesser degree). The effect persisted for 4 hours. Furthermore, fasting rats produced more than twice as much orexins as rats feeding freely. For this reason, the molecules were names "orexins", after the Greek word orexis, which means "appetite". They speculated that the orexin-secreting neurons might somehow be modulated by glucose.
At the same time, another group of researchers using a completely different approach found that the same group of hypothalamic neurons were stimulated by a peptide hormone similar in composition to the gut hormone secretin. They identified the same prohormone and its two peptides, naming them hypocretins for "hypothalamus" and "secretin". They found that at least one of the peptides had a neuroexcitatory activity in specific areas of the brain (they mapped effects in the hypothalamic neurons, the posterior hypothalamus, the septal nuclei in the basal forebrain, the preoptic area, the paraventricular nucleus of the thalamus, the central gray, the locus coeruleus, the colliculi, the laterodorsal tegmental nucleus, and the nucleus of the solitary tract) suggesting that the peptides acted within the central nervous system as homeostatic regulators with a role in nutritional homeostasis.
Scientists have not decided on whether to call them orexins or hypocretins yet, so both are used. They are found in all vertebrates.
Mammalian orexin A sequences thus far identified (human, rat, mouse, pig, dog, sheep, and cow) are all identical, whereas the sequences of orexin B show some differences among species. From Orexin/Hypocretin: A Neuropeptide at the Interface of Sleep, Energy Homeostasis, and Reward System, Natsuko Tsujino and Takeshi Sakurai
In 1999, a group of scientists found that narcolepsy (a sleep disorder characterized by extreme daytime sleepiness) was caused by a lack of a hypocretin/orexin receptor 2 gene in certain dogs, therefore establishing that they play a very important part in the regulation of wakefulness.*
Since then, an enormous body of work has shown that orexins/hypocretins (O/H from here on in) are involved in the regulation of a wide range of behaviors, including wakefulness and vigilance (needed to find food), systems that regulate emotion and reward (including drug-seeking behavior when stressed and eating for pleasure - "consumption beyond homeostatic needs" - leading to obesity), and more.
What does eating have to do with sleepiness?
Several studies report that the firing rates of O/H neurons are influenced by serum glucose, triglycerides and amino acids.
In English: You are awake (O/H is being secreted by O/H neurons in your hypothalamus). You eat. Your serum glucose rises. The elevated glucose causes depolarization of inhibitory neurons that hyperpolarize O/H neurons decreasing the amount of O/H. released. Result: wakefulness decreases.
Control of Cerebral Blood Flow
The Gastrointestinal Circulation.
Comparing these two papers - the first and second references - is a wonderful example of the completely different methods used by scientists to investigate unknowns and up with the same basic conclusion.
Orexins and orexin receptors: a family of hypothalamic neuropeptides and G protein-coupled receptors that regulate feeding behavior, Cell 92 (4): 573–85
The hypocretins: Hypothalamus-specific peptides with neuroexcitatory activity Proc. Natl. Acad. Sci. U.S.A. 95 (1): 322–7
The Sleep Disorder Canine Narcolepsy Is Caused by a Mutation in the Hypocretin (Orexin) Receptor 2 Gene
The role of orexin in motivated behaviours A Nature Neuroscience Review
The role of orexin-A in food motivation, reward-based feeding behavior and food-induced neuronal activation in rats
*Human narcolepsy - caused by a destruction of O/H neurons - also is associated with metabolic abnormalities, including increased frequency of non-insulin-dependent diabetes mellitus and increased body mass index.
Hypothalamic Orexin Neurons Regulate Arousal According to Energy Balance in Mice
Orexin/Hypocretin: A Neuropeptide at the Interface of Sleep, Energy Homeostasis, and Reward System